In no particular order:
1) World of Warcraft (best ever implementation of MMORPG)
2) Guild Wars (MMORPG/CORPG... and it's FREE monthly
)
3) Battlefield 1942/Battlefield 2
4) Unreal Tournament/ 2k3/ 2k4 (best... EVER... team based online fps)
5) PlanetSide (MMOFPS... good idea, great implementation, and when you get continental battles... oh my... ;D)
6) Doom series (nuff said)
7) Half Life/ HL2 (best ever FPS, hands down. HUGE story, always pushed the limits of available technology at the time and there's more coming ;D )
8) Final Fantasy series (need I really say more? No? good)
9) XenoGears (in my mind, one of the greatest singlular RPGs ever)
10) Metal Gear Solid series (makes you feel like a real special ops dude :warstory
Honorable mention: Xenosaga 1 & 2 (great story, game okay), Gran Turismo series (best driving games ever), Lifeline (so far, the only completely voice controlled game I know of that actually WORKS), SSX series (wacky, fun, out there... great games), Metroid Prime series (AWESOME games), Legend of Zelda series (excluding 3DO games), F-Zero GX (you want high speed gaming, this is like a crack-addict's game), Soul Calibur series, Beyond Good and Evil (hugely awesome, but for some reason... is too short)