Give me a FPS and I'll play it. Still, I'm a diversified gamer. As for my all-time 5 favorites (1 max per series):
Halo: Combat Evolved (Xbox) ~ Changed the genre more than any game since Doom. (Note: Halo 2, 3, ODST, Reach would also be on my list if not for my self imposed restrictions)
Pokemon Gold/Silver ~ (GBC) Yeah, I'm not afraid to say it. These games were awesome. Add in Mewtwo from Red/Blue and you were unstoppable.
Return to Castle Wolfenstein (PC) ~ This baby beats out its predecessors because of its class based online play. On PC, it was great. If you were lucky enough to DL it on your Xbox 360 before it got taken off, I tip my hat to you.
Caesar II (PC) ~ Never hear of it? That's not too surprising. Released around the same time as Roller Coaster Tycoon, the object of the game was to build a city inside of a Roman province while expanding the Empire through war. It was a complicated game then, and though there were some glitches, its still enjoyable today. (See: "Plebs are needed!")
Ultimate Doom for Windows 95 (PC) ~ If you or someone in your family bought a computer shortly after the release of Windows 95, you got this version of the game. Paired with the D!Zone Gold expansion pack, it was impossible to get tired of playing.
Now I won't say that these are the best games I have ever played, but they certainly made the biggest impressions on me at the time of release. Games like
Unreal (PC),
Half-Life (PC),
Double Dragon (SNES),
Goldeneye (N64),
Super Mario Bros. (NES),
Super Smash Bros Melee (GC),
F-Zero (SNES),
Call of Duty: Modern Warfare 2 (PS3),
Tetris (TI-83),
Tomb Raider (PC),
Donkey Kong Country (SNES),
Clannad (PC, Xbox 360 versions
), et al have left good impressions on me.