Some of my epic and deep favorites:
I Was Born for This by Austin Wintory from Journey OST
Hills of Radiant Wind from NieR Gestalt & Replicant OST
Kline's Dream from Alundra
Staff Roll (Credits Theme) from Tekken Tag Tournament
Atop the World by flashygoodness from Tower of Heaven OST
Tony Hawk's Pro Skater was the one that first came to mind. Although Final Fantasy has some great songs on, also.
Superman by Goldfinger from Tony Hawk's Pro Skater
Note for Chrome users who can't see embedded Youtube videos: See the right end of the address bar. There's a little gray shield. Click it. Click "Load unsafe scripts". Voila. (Have to do it repeatedly though. Limitations of outdated board code, I suppose.)
Ken's Theme from Super Puzzle Fighter 2 Turbo
New York City from Teenage Mutant Ninja Turtles, The Hyperstone Heist
Final Fantasy DropWish (FFXIII-2, Main Theme) by Masashi Hamauzu
Balamb Garden (FFVIII) by Nobuo Uematsu
Because You're Here (FFXIII) by Sayuri Sugawara
Breezy (FFVIII) by Nobuo Uematsu
Legend of the Great Forest (FFV, Japanese Ver.) by Nobuo Uematsu
I've been really disappointed in the weather lately. This should add some color to the skies.
Chasing All My Dreams (Ridge Racer 6) by Hiroshi Okubo feat. Sunny Hilden
I can't believe I forgot to include this in my Final Fantasy drop...
Theme of Love (Final Fantasy IV) by Uyama Hiroto