I'm stuck between the big three of the 90's...Mario, Zelda and (classic) Sonic...
Then again, RPG-wise Breath of Fire is an excellent series and fighting-wise I'm stuck between Soul Calibur and Super Smash Brothers. Hmm
Of all time I can't say, but for fighters it'll have to be Super Smash Bros, Adventure will Be Legend of Zelda (Majora's Mask was awesome considering its humble roots), platformer I can't decide, FPS is Doom without a doubt and puzzle is Tetris (yes it's a series as some of the games have been different enough to be considered seperate)