Final Fantasy 7 is definitely my favorite; I'm sure plenty will agree if FF7 is remade for PS3 it will revolutionize the console. The entire Final Fantasy series has been excellent, along with Star Ocean, Kingdom Hearts, and plenty of other RPG's I really can't recall right now...
However I often find myself playing Modern Warfare (soon to be Modern Warfare 2) on XBox Live. Being in the military, I've actually fired many of the weapons portrayed in that game and it's more true-to-life than people give it credit for. I guess that'd be my favorite "not-an-RPG" game.
My favorite game would be "Beyond Good and Evil". It holds a special place in my heart for making me realize that games can be beautiful. The funnest game I've ever played would be Brutal Legend. You can melt people's faces with a guitar solo named the Facemelter. AWESOME METAL!!!!!
Try FPS like FEAR, QUAKE4 & DOOM 3!
These games got high rep hehehe, best played when lights are off & use ear phones for sound output... wahahahaha....
For MMORPGS I recommend CABAL Online... Nice graphics & Special Effects....
Skies of Arcadia for the dreamcast. Nothing felt so good and being a skypirate in an rpg that also had airship battles FTFW.
Secret of Mana I still play this on my SNES.
FFVII
Darkcloud
And one that most everyone has never heard of. Eternal Fantasia. Before Giutar Hero's this game had a music playing part to the game that was very much like that. Lots of fun, oh and it is an rpg too.