In chronological order...
i) Elite on the BBC - this is where it all started for me; a whole galaxy to explore, vector graphics, market trading and lazers!
ii) Doom - i know Wolfensein was first but this was just so polished; the source of fps.
iii) Carmageddon - no game has made me laugh and cackle so much. Just loved driving like a nutter then sitting back and watching the tv replay.
iv) Half Life (and it's successors). Raised the bar.
v) Grand Prix Legends (and it's spiritual successor GTR2 with the Power and Glory mod) - Aces High with 1950's cars... what more do you want? A very dedicated and truly gifted community, props to simbim for the modablilty and no legal hassles. Note P&G v2.0 out, it is stunning.
vi) Aces High - came here from one of the early fighter aces, world of difference. Can still recall the sense of "this is it!" Ever since zx81 flight sim (the one with no landscape just instuments and a landing strip) Aces High provided that which I had dreamed of.
vii) Deus Ex - RPG and FPS.. choices.
viii) Rome Total War - There used to be a show on telly where the contestants would fight historic battles as the commanders of an army against an AI. They were playing RTW about a year before it was released!!! Combine Civ4 with tactical battleground control and it's got to be a winner.
ix) Team Fortress 2 - Something for everyone. The replayability of this shooter is astonishing. You never know what is going to happen next. Incredibly funny, challenging and charming. Aspects of AH when your team goes from absolute losers to holding their own to winning. I just find it exciting.
x) Fallout 3 - yes bug problems but still this is one of the greatest games I've played in a long time. Complete freedom of choice. And the gameworld.. it is almost awe inspiring the level of detail and crafting that has gone into it. Completely moddable, runs like a dream on old hardware - this is only the start, so much more to come from the modders.