Sorted by year...
If you think some of my choices on this list are completely wrong, let me know in the comments.

1984:
Nausicaa Of The Valley Of The Wind
One thousand years after the Giant Warriors caused an apocalyptic event known as the seven days of fire, humans are living in constant fear of the Toxic Jungle. This ever-spreading forest is filled with poisonous plants and gigantic monstrous insects; even the very air is deadly. Nausicaa is the kind and wise princess of a small, peaceful country known as the Valley of the Wind, which has so far avoided the spread of the forest. One night a large airship containing one of the Giant Warriors crashes into the valley. The following day soldiers from the powerful nation of Tolmekia invade the Valley of the Wind to reclaim and revive the warrior. As the only one who truly believes that there is a way for humans to live alongside the insects, Nausicaa must find a way to stop the war that now threatens her people and protect the Toxic Jungle before the Tolmekians burn it to the ground.
1985:
Mobile Suit Zeta Gundam
The year is Universal Century 0087, and mankind has yet to be liberated from Earth's gravity. Seven years since the end of the One Year War, tensions between the Earth Federation and the space colonies continue on the rise. The police actions of the Titans, the Federation's military arm in space, fuel anti-Earth sentiment throughout the colonies and give rise to the Anti-Earth Union Group. Kamille Bidan, a young spacenoid from Space Colony Noa, soon finds himself in the middle of this armed conflict and behind the cockpit of the Titans newest weapon: the Gundam Mk-II.
1986:
Dragon Ball
A mysterious monkey-tailed boy named Goku teams up with a teenage computer-wiz girl named Bulma to search for the mystic Dragon Balls. According to legend, whoever collects all 7 Dragon Balls will have any one wish granted. Join Goku in this hilarious anime masterpiece, as he races and battles to save the world from the forces of darkness. Who will find the balls first?
1987:
Wings of Honneamise
Shiro Lhadatt wanted to fly jets for the Kingdom of Honneamise's Air Force when he was young, but unfortunately he didn't get the grades he needed; instead, he enlisted in the Space Force, a tiny embryonic unit that most people haven't even heard of. Embittered and disillusioned about his lot in life, Shiro takes no interest in his training - that is, until he meets and gets to know a young woman preaching God's word on the city streets. After one inspiring conversation with her, Shiro promptly sees the light; he finds his passion for flight reinvigorated and immediately volunteers to be the pilot for his unit's first space warship! Reaching that new frontier is all well and good but Shiro still faces some major obstacles: even if launching the first space warship becomes reality, not everyone will be happy to see the Space Force succeed. Suddenly, Shiro has to grapple with the complex, far-ranging consequences of his very personal decision.
1988:
Grave of the Fireflies
With their father serving overseas in the Navy towards the end of the World War 2, Seita and his younger sister Setsuko are living as normally as they can. One day during a firebomb raid on the city their mother suffers fatal wounds and the two siblings' lives are turned upside down as they go to live with a relative. After suffering the cruel treatment of their aunt, who makes it clear that their very presence is a nuisance, Seita and Setsuko decide to leave and go to live in an abandoned bomb shelter. With no one else to rely on, Seita and Setsuko try their hardest to live from day to day. Though when food becomes ever more scarce and no one is willing to sell what little provisions they have, life for the pair is increasingly difficult. Then when Setsuko falls ill, Seita begins to realize just how fragile life is...
1989:
Dragon Ball Z
Five years have passed since Goku and his friends defeated Piccolo Jr. and restored peace to the planet. Gohan - Goku's son - and a variety of good, bad, and morally ambiguous characters are back, and perpetually not ready for action! Aliens, androids, and magicians all hatch evil plots to destroy the world and it's up to Goku to save the Earth once more - that is, once he and his comrades train plentifully in preparation. Enemies will become friends and power levels will rise to unimaginable levels, but even with the help of the legendary Dragon Balls and Shen Long will it be enough to save Earth from ultimate destruction?
1990:
Dragon Ball Z Special 1: Bardock - The Father of Goku
Bardock, a low-class Saiyan warrior, is struck by an alien during his mission. Shortly afterwards he is tormented by strange and haunting visions about the destruction of a planet. During the events that follow, however, he suddenly realizes that what he is seeing through these visions is none other than the future of his own people, the Saiyans. Starting from that moment he sets out to do everything in his power to escape his fate and the fate of his world...
1991:
Dragon Ball Z Movie 5: Cooler's Revenge
After the defeat of Freeza, it looks like Goku and his friends will finally get to enjoy some quality rest and relaxation... or will they? Freeza's older brother Coola has learned of his death, and vows to take revenge against the Super Saiyan. When Coola and his minions disrupt our heroes' camping trip, Goku looks like he's seen a ghost! This time, the battle is personal, and Goku must once again rise to the occasion to protect the Earth and his friends.
1992:
Yu Yu Hakusho
Yusuke Urameshi was a normal middle school punk until he was hit and killed by a car, while saving a child. His selfless action earned him the right to gain his life back and serve as a detective of the spirit world, keeping the world of the living safe from a myriad of demons. But being reborn has its price: Yusuke must hatch a spirit beast that will develop according to his actions, and if he doesn't act in a good and honest manner, it will eat his soul. Can Yusuke protect the human and spirit worlds and still manage to save himself in the process?
1993:
Ninja Scroll
Jubei Kibagami is just a wandering swordsman minding his own business... until fate lands him in the middle of a battle with the terrifying Devils of Kimon! Now the fate of all of Japan lies in the hands of a vagabond samurai, a deadly female ninja and a perverted old monk as they take on an enemy who is, literally, immortal.
1994:
Dragon Ball Z Movie 10: Broly - Second Coming
While out collecting dragon balls, Goten, Videl and Trunks stumble upon a small village that has been under frequent attack by a monster. Our friends are more than happy to help the villagers out, but what they don’t know is that deep within the icy mountains lies an even greater threat – a warrior that has been asleep for seven years. Brolly, the Legendary Super Saiyan, is back. Still thinking only about Goku he ravages the land, fighting the present Z-Warriors until they can fight no more. Will the gang be able to once more withstand Brolly’s powerful attacks?
1995:
Neon Genesis Evangelion
In the future, a devastating event known as Second Impact has destroyed Tokyo as we know it, giving rise to Tokyo III - a city under siege by mysterious lifeforms known only as Angels. Mankind's only line of defense are the Evangelions, a set man-made machines piloted by a trio of fourteen year-old teenagers, Rei, Shinji, and Asuka. The fate of Japan and the entire world now lie with these three children, though they might not have the power to save the most important thing of all: each other.
1996:
Mobile Suit Gundam 08th MS Team
War between the Earth Federation and Zeon has ground to a bloody standstill, and both sides eagerly seek a quick resolution. Among these is Ensign Shiro Amada, a young mobile suit pilot for the Federation assigned to the 08th mobile suit division in the heart of the Vietnamese jungle. The members of his team include Karen, a hot-headed pilot and part time mechanic; Sanders "The Reaper," a pilot with a reputation for getting the people in his unit killed; Eledor, an aspiring musician, flirt, and communications officer for the team; and Mikel, the love-struck driver for the team's command vehicle. As the gravity of war bears down on their shoulders, they must struggle to keep their sanity amidst a chaotic battlefield that continually tests their wit, focus, and resolve.
1997:
Berserk
Born beneath the gallows tree from which his dead mother hung, Guts has always existed on the boundary between life and death. After enduring a terrible childhood, he spends his adulthood in brutal combat, pitting his strength against others in order to build his own. Life is simple enough for Guts until he meets Griffith, the inspirational, ambitious, and beautiful leader of the mercenaries, the Band of the Hawks. When Guts loses to Griffith in a duel, he is forced to join the group, and, despite himself, finds a sense of camaraderie and belonging amongst them. However, as Griffith leads his soldiers from victory to victory, the bloody wars and underhanded politics reveal a side to him that nobody quite expected. Can Guts, a simple warrior, defend those who have come to mean the most to him, all the while struggling not to lose to the darkness he has carried with him his entire life?
1998:
Cowboy Bebop
Follow interstellar bounty hunters Spike Spiegel and Jet Black as they scour the galaxy for criminals with prices on their heads. Hoping to escape their past, they live on the spaceship Bebop, but it's a dangerous business and old enemies don't forget easily. Allies come from unlikely sources, however, as they find comrades in the beautiful swindler Faye Valentine, the genius child hacker Ed and the genetically engineered 'data dog' Ein. Will they be able to help each other though their respective struggles, or is their fate really inevitable?
1999:
One Piece
Long ago the infamous Gol D. Roger was the strongest and most powerful pirate on the seas. As he was about to be executed he revealed that he hid all of his wealth, including the legendary treasure known as One Piece, on an island at the end of the Grand Line - a treacherous and truly unpredictable sea. Monkey D. Luffy is a spirited, energetic and somewhat dim-witted young man with a very big dream: to find One Piece and become the Pirate King! However Luffy is no ordinary boy, as when he was younger he ate one of the Devil's Fruits and gained its power to become a Rubber Man. Now in this grand age of pirates Luffy sets out to gather a crew and sail to the most dangerous sea in the world so that he can fulfill his dream... and maybe even his appetite!
2000:
FLCL
Naota Nanbada is a boring young boy who leads a boring life in a boring town. His older brother has left for America, and the closest he comes to any excitement is when his deadbeat dad has too much sake. But things change one day when a bizarre girl zooms up to him on a scooter and smacks him in the face with her guitar. What's more, once Naoto returns home he discovers that this strange woman has arrived ahead of him and moved in! Not only does she constantly engage in perverted activities with Naota's father and flirt with the young man himself, but she also claims to be an alien who is searching for the ‘Pirate King.' Now, Naota must learn to live with this new intruder, deal with an odd government agent who sports exceptionally large eyebrows and the mysterious Medical Mechanica, and come to terms with the fact that there are a variety of robots and weapons emerging out of his head - amongst other things. Perhaps boring wasn't so bad after all...
2001:
Hellsing
In present day England, a war is being fought. The average citizen does not notice, but vampires are running rampant among the populace, and it's up to the Hellsing organization to contain the bloodsucker threat, using even their own weapons against them. Alucard, a vampire himself, is the best agent the organization has to offer, answering only to Integra Hellsing herself. No one knows much about this mysterious figure fighting against the occult, but things starts to change after he “recruits” a new agent to the establishment...
2002:
Full Metal Panic!
Gonzo does it again with this action-packed mecha comedy. She's an ordinary high school girl. He's a counterterror agent assigned to protect her from those who would steal the information locked in her mind. OK, so she's not so normal after all. Armored Slave battles and lovers' spats abound as Sousuke and his comrades try to track down the mysterious Gauln before it's too late.
2003:
Fullmetal Alchemist
Once upon a time, two brothers passed the happy days of their childhood by studying alchemy, which is governed by the equal transfer principle: an eye for an eye -- you can't get more than you give. But these brothers tried to defy that law, and a horrific accident resulted. Now, the older brother, Edward, is called the Full Metal Alchemist because of his metal limbs, and the younger, Alphonse, is a soul without a body, trapped within the confines of an automaton. Together they search for the power to restore themselves, to find the lives they lost so long ago...
2004:
Howl's Moving Castle
The responsible Sophie led a relatively normal life, safe within the walls of the hat shop in which she works; for outside, it is rumored, the evil wizard Howl roams the land in his mobile black castle. After a chance and mystical encounter, poor Sophie finds herself transformed by a spell which makes her appear to be an old woman, and thus embarks on an adventure to find Howl’s castle and put an end to her curse. A mystical world of talking flames, sentient scarecrows and magic aplenty awaits those who seek the legendary Howl...
2005:
Full Metal Panic! The Second Raid
Half a year has passed since Sousuke Sagara took up the job of protecting Kaname Chidori and has started living like a normal teenager for the first time. A former child soldier, his view on the perils of everyday life is highly unconventional and in frequent need of violent adjustment; Kaname can only hope her endless assault will eventually get him used to normal life. But a shadow looms over their happy days as Sousuke's employer, the private army called Mithril, is attacked by a new unknown enemy. Suddenly outgunned, can Mithril afford to keep one of their best playing around?
2006:
Black Lagoon
Rokuro Okajima is a small-time salaryman who is carrying documents for his company, when the ship he's traveling on is attacked by pirates. Kidnapped, he discovers to his dismay that his employers' main concern is to ensure the documents don't get into the wrong hands, even if it means sending the carrier to the bottom of the sea. Now, with his former life ruined and his kidnappers seeming comparatively friendly, "Rock" decides to join their merry band of mercenaries, and sets out with a new career to the shadier corners of the South China Sea.
2007:
Tengen Toppa Gurren Lagann
Simon lives a boring life in the underground village of Jeeha, where his main job day in and day out is to dig tunnels. His close friend Kamina, however, longs to bust out of their oppressive existence and reach the surface world where open skies and adventure await! One day, during his usual digs, Simon discovers a robot with a big face buried amongst the rocks. No sooner has he shown Kamina his mysterious find when two beings from the surface crash land into Jeeha Village - one is a gun-toting woman calling herself Yoko and the other is a terrifying mecha piloted by a Beastman! Seeing their chance to escape village drudgery, Kamina rallies Simon and Yoko to defeat the invader using their new robot, Lagann. However, upon breaking out onto the surface world, Simon, Kamina, and Yoko encounter enemies more powerful than they could have envisioned. Their fight for adventure just turned into a war for the survival of the human race - will their lust for freedom hold out against such terrible odds?
2008:
Kara no Kyoukai Movie 5: Mujun Rasen
Shiki meets a boy named Tomoe Enjou, a runaway who claims to be a murderer. Shiki allows Tomoe to use her apartment as his hideout. And from that day onward, their strange cohabitation begins. But then one day, Tomoe sees his mother whom he's sure he's killed. Shiki and Tomoe head for the Enjou residence in the Ogawa Complex where the two see Tomoe's parents alive! There Shiki encounters a mage named Souren Araya and finds that he is the mastermind behind all of the incidents involving her up to then. Shiki finds herself trapped within spirals of paradox. And this is only the beginning of a vicious plot by Souren Araya, the powerful sorcerer and archrival of Touko.
2009:
Fullmetal Alchemist: Brotherhood
The foundation of alchemy is based on the law of equivalent exchange; you cannot produce something from nothing. As such, alchemy is bound by one taboo - human transmutation. Four years ago two young brothers, Edward and Alphonse Elric, broke this taboo when they tried to resurrect their dead mother. During the process Al's body disintegrated and Ed lost his leg. In a desperate attempt to prevent his brother from disappearing completely, Ed sacrificed one of his arms so he could affix Al's soul to a suit of armor. When his missing limbs are replaced by auto mail parts, Ed bears the name of the Fullmetal Alchemist - the youngest ever State Alchemist and dog of the military. Now, alongside his brother, Ed uses his status within the military to attempt to find any way that he can return their bodies back to their original state.
2010:
Mardock Scramble: The First Compression
To stop the unstoppable you need the irresistible. To kill the un-killable, you need someone for whom death no longer has a meaning. And to catch the perfect serial killer, you need the one person who knows his methods the best… his last victim! Murdered and reborn, no longer human, the female cyborg named Balot exists for one reason: to track down the man who killed her and bring him to justice.
2011:
Steins;Gate
The eccentric mad scientist Okabe, his childhood friend Mayuri, and the otaku hacker Daru have banded together to form the Future Gadget Research Laboratory, and spend their days in a ramshackle laboratory hanging out and occasionally attempting to invent incredible, yet generally useless, futuristic gadgets. However, their claymore is a hydrator and their hair dryer flips breakers, and the only invention that’s even remotely interesting is their Phone Microwave, which transforms bananas into oozing green gel. But when an experiment goes awry the gang discovers that the Phone Microwave can also send text messages to the past. And what's more, the words they send can affect the flow of time and have unforeseen, far-reaching consequences...
2012:
Space Brothers
When Mutta and Hibito were children, they made a promise to become astronauts together after spotting a UFO one night. Now adults, the duo's path couldn't have diverged more – Hibito is about to travel to the moon with NASA to help simulate the future exploration of Mars, and Mutta is unemployed, having recently headbutted his boss at an auto company. Still, the man can't shake his desire to surpass his younger brother, and soon, he becomes an applicant for Japan's JAXA space program. His ultimate goal, to get one step ahead of Hibito and go to Mars. But the path to becoming an astronaut is long and fraught with tests and challenges. Will Mutta and newfound friends Kenji and Serika manage to persevere and achieve their dream?
2013:
Sakasama no Patema

Patema lives in an underground world and, although she is a princess, she is held back by the rules imposed by the elders of her clan. One day when she is exploring a forbidden zone she tumbles headlong into a void and out into the wide open world above the surface, a place with reversed physics where she could “fall up” into the sky and be lost forever.
Age is a student on this surface world and a part of a society whose compliant population has been brainwashed against the “sinners who fell into the sky.” When he spies Patema hanging upside down from a tree, he pulls her down to safety, struggling to keep her earthbound as she grips on to him for dear life. Together they master the art of navigating competing gravitational forces and set out to discover the secret that keeps their worlds apart.

2014:
Zankyou no Terror
On a summer day, a massive terrorist bombing suddenly struck Tokyo. The culprits behind the act that woke up this complacent nation from its slumber, were just two boys. Now, the culprits known as "Sphinx" begin a grandiose game that encompasses all of Japan.
2015:
Shokugeki no Souma
Food Wars! Shokugeki no Souma centers on Yukihira Souma, a middle school student who is determined to surpass his father’s culinary skills. One day, his father decides to close down their family restaurant and hone his skills in Europe. Before leaving, he enrolls Souma in an elite culinary school that is extremely difficult to enter with a graduation rate of only 10 percent. Will Souma be able to improve his skills, or will the kitchen prove to be too hot?
2016:
Boku dake ga Inai Machi
Satoru Fujinuma is a reclusive part-timer with no plans for the future. What sets him apart from the other slackers in his town is an involuntary time travel ability that allows him to jump back several seconds in time in order to prevent accidents and even deaths. As incidents around town begin reminding Satoru of a childhood trauma he'd sooner forget, he finally begins to question what caused his ability to surface and whether or not it's powerful enough to change the past.