Favorites, by Genre:
RPGs
PCRPG: Somewhere split between the Wizardry series and the Ultima series, while they were both alive, historically I think the ending trilogy for Wizardry (6, 7, 8) was an amazing gem in the crown, Planescape: Torment gets a special mention for being amazing.
JRPG/CRPG: Phantasy Star 4, Phantasy Star 2, Chrono Trigger top the list, FF6 and SMRPG below them.
MMORPG: They all have their place, but the player bases change means the quality of the games change too... EQ, UO, and The Realm all get special notes, and WoW gets a small prize for most time spent in a single MMO.
MORPG: PSO, hands down. May be changed to PSO2 if SEGA can get lightning to hit the rod twice. Spiral Knights is worth a mention for being check-out worthy.
SRPG: FFT and Shining Force. Disgaea 1 too.
Capture/Collection RPG: DQM, Pokémon 1st/2nd gen, Monster Rancher 2.
ARPG: King's Field. This genre is a little broad, but there ya go.
Shooters
FPS: Heretic, Hexen, Hexen 2. For those that count these as Hybrid games, my answer would then be Ultimate DOOM.
Competitive FPS: Quake 2.
TPS: Probably not one here... I guess I'd slot Heretic 2 or Deus Ex: Human Revolution here if I was forced.
Sh'mup: The Gradius/Parodius Series.
Run'n'Gun: Contra series, esp. Hard Corps. and Neo. GODS is underrated.
Action
Platforming: Sonic 2, SMW, SMB2(US), Cool Spot, Prince of Persia
Hack'n'slash: another broad category, Dynasty Warriors and Chaos Legion can fill this space, though.
Beat'em'up: Streets of Rage, Golden Axe, ALTERED BEAST WOO!
Racing
ARC: Ridge Racer
Simulation: No one likes simulations, go away. Freak.
Multiplayer: Mario Kart 64
Combat: Twisted Metal, but Mario Kart 64 qualifies here as well.
Getting bored... may come back and update/finish this, might not. Here'sa dump of some games of worthy mention that either don't fit into the above categories or lost out to something up there, in no particular order:
DUNGEON DEFENDERS, seriously, go buy this game it's awesome. (But if you have the option, get the Steam version, it's the only one that's constantly updated.)
The Lost Vikings, Deus Ex, Marathon, Team Fortress 2, Portal, Exile 3, Helherron, Might and Magic (*NOT* Heroes of Might and Magic, those suck), Chip's Challenge, Wizardry: Nemesis, SSB, SSBM, LoZ2, Etrian Odyssey, Mystic Heroes, Fantasy General, Warlords 2.
