I've put off doing this for a while so here it goes:
I decided to make the list by system so you wouldn't make such a big mess by trying to play across so many platforms.
XBox:
Steel Battalion ( Awesome game, the controller sinks you right in)
Knights of the Old Republic (Reason I bought an Xbox)
Oddworld Stranger's Wrath (I really like the art design of this series)
One of the Splinter Cells ( I couldn't choose since I like them all, I would probably go with Pandora tomorrow)
Gta: Vice City or San Andreas (San Andreas is HUGE, but I prefer Vice City's story)
PsX:
Castlevania Symphony of the Night (Classic Game that holds it's replay value)
Final Fantasy Tactics (I LOVE this game)
Tactics Ogre (I LOVE this one too)
Xenogears ( A good RPG if you're hankerin to play one)
Chrono Chross ^^^^ I'd pick this one over the other one tho
Ps2:
Final Fantasy X (I'm not a fanboy, maybe I am, but I do love the Sphere Grid system and Blitzball)
Disgaea (You will never tire of this game, at least I haven't)
Devil May Cry ( This game was/is great, Part 3 comes close but I prefer the original
Metal Gear Solid 3: Subsistence ( It's MGS 3, with more shit, need I say more?)
Klonoa 2 or Sly Cooper ( Both of these are awesome platformers with 2 distinctive styles, If you ever decide to part with Klonoa, I'll take it
)
GCN:
Star Wars Rogue Squadron 2: Rogue Leader (This game has some hard ass levels but you feel like you accomplished something when you beat it)
Eternal Darkness: Sanity's Requiem ( this game is so awesome, play at night with the sound turned up, a memorable experience to say the least)
Resident Evil 4 (absolutely brilliant play at night, sound blaring, and prepare for gaming nirvana)
Mario Kart: Double Dash (hours upon hours of fun!)
Metroid Prime 2: Echoes or Legend of Zelda: Wind Waker ( Both of these are solid titles, just pick whatever you're in the mood for)
I can't really help on the GBC/GBA games since I doubt I have completed more than a handful of 'em.
And as for GEN/SNES play 'em all. You won't be dissapointed.
Good Luck and Happy Gaming!
GMOOJ