PC----> System Shock 2
ARC---> Time Crisis 3
NES---> Super Mario Bros. 3
SNES--> Super Mario World
N64---> Legend of Zelda: Ocarina of Time
NGC---> Super Smash Bros. Melee
WII---> Legend of Zelda: Twilight Princess
GB----> Pokemon Blue/Red/Yellow
GBC---> Pokemon Gold/Silver/Crystal
GBA---> Final Fantasy Tactics Advance
NDS---> Final Fantasy III
GEN---> Shining Force 2
DC----> Shenmue
PS1---> Final Fantasy Tactics
PS2---> Final Fantasy X
PS3---> Played a few but don't have one yet because the exclusives I've played are mediocre (will probably be Final Fantasy XIII though ;D)
PSP---> Final Fantasy Tactics
XBOX--> Halo
360---> Call of Duty 4: Modern Warfare
this post makes me look like a huge Zelda/Final Fantasy fanboy, but truth of the matter is on a grand scale of EPICness most shooters and fighting games lack depth, story telling and other qualities that make the game a memorable thing for me. There are some stellar examples that do stand out however (System Shock 2, SSBM, Halo, and CoD4). It's not that I don't enjoy fighters or fps i do, thoroughly, but they tend to not have as much content as grand scale rpg/adventure games.
EDIT: This was probably the hardest time I've ever had posting, simply due to the fact that I promised myself I would not have any tie games or mention any runner ups