My favorite anime, without a doubt, would have to be Revolutionary Girl Utena. It was the first anime I ever really got into, so it holds a special place in my heart. There's so much about it, from the imagery to the music to the complex characters and relationships that make it stand out. Many might argue that it is a very weird anime, but I think if you look past the fact the it's a little strange, you will realize that even the writers of this deep and interesting narrative don't take themselves too seriously. Most of all, what really touched me was Utena's relationship with Anthy. It's really a beautiful story and I've even heard many fans say that the anime is much better than the manga. I haven't read the manga, however, so I really can't say.
Animos wrote:
In no particular order:
Fullmetal Alchemist & Brotherhood
Princess Tutu
Puella Magi Madoka Magica
Ghost in the Shell
Wolf's Rain
I'd probably have to say Fullmetal Alchemist is my favorite mostly because its what got me into anime all those years ago and is still kind of the standard for what I want in a good anime series: not too long, concise story, well rounded characters, good mix of humor and action, and an interesting and unique world.
I never really thought about the benefits to the original Fullmetal Alchemist anime as opposed to Brotherhood. I suppose that is far more accessible to new fans and very nostalgic for many of us. I still personally prefer Brotherhood, but maybe that's because it filled in a lot of blanks for me because I had so many questions when I first watch the original anime.