I'll list some varied songs from my childhood and recent years, not in chronological order:
If There Were Any Other Way - SCII in Arcade Mode, and perhaps SCIII in Tales of Souls Mode (High-Pitched Destined Battle 1 Remix)
Water Dance (Xianghua's Theme with Erhu Intro) - SCIII
Blinded in Chains from Avenged Sevenfold (Uncensored Lyrics Version)
Hand of Blood from Bullet for my Valentine (Uncensored Lyrics Version in both Burnout Revenge and Most Wanted 2005)
Snow Blind Detected Theme, Austrian Alps (Multiplayer Map Theme)
Everything or Nothing Theme
Fighting in Built-Up Areas from Ladytron (Kenji's Theme in NFS Carbon if playing as Tuner, Bulgarian)
Stick Em'Up from Quarashi (Uncensored Full Lyrics and Spanish Intro, probably in the intro of NFL Blitz 2003 and as a full cut song in ATV Offroad Fury 2)
Battlestations Midway/Pacific Menu Theme Mashup (Separate but respective menu themes, now you hear the U.S./JP instruments in harmony with each other)
Tokyo Nights (Song from Burnout 1 played in Burnout Paradise and Remastered)
Tokyo Race from Cars 2 (Almost sounds like the first few seconds of Momaeler from Tokyo Xtreme Racer 3)
Tyga from Diamond Life (Only heard during a race, even when chased from NFS Undercover)
The Qemists - No More from NFS Rivals (Only heard during free-roam head-to-head races as a Racer)
Pursuit Max Heat from Need for Speed 2015 (Despite the theme's name, you can hear it at Heat 3 or higher)
Where Springs Not Fail (Leixia's Theme from SCV)
MEC Loading Theme (BF2/BF3 Back to Karkand Mashup)
The Sims 3 Theme Remix Electronica by The Young Punx!, Original by Steve Jablonsky
UT2004 Main Menu Theme by Will Nevins, Starsky Partridge, and Kevin Riepl in HD
UT2003 Main Menu Theme by Kevin Riepl (In UT2004, if you somehow changed the music files around, you'll hear this instead too)
The Elder Scrolls V: Skyrim (Dragon Fight 1 and 2)
Dragon's Dogma - All 3 Vanilla Battle Themes
À cause des garçons (Riot in Belgium Remix, French)
Even with Google Translate, I can't keep up with what they're actually saying, it sounds like butchered Japanese and French to me, EA didn't need to censor it at that time.
Junkie XL - Action Radius from NFS Underground 2003
Jumpin' Jammin' (Phantom 9's Theme) from Import Tuner Challenge
Although it is HD, the background is blank, and it's the only one I found so far. That boss nearly had me in there when I met him with my max tuned starter car with a huge winning streak, especially that lightning effect.
Halo 2 - Peril Cover (Menace) CONTACT: HARVEST
Halo 2 and 3 - Leonidas
Halo 3: ODST - Wildlife (Only heard in last wave of Firefight, occurs randomly at start of set)