RTS -
C&C Red Alert 2 (C&C 3 has better graphics, etc, but IMHO worse storyline).
Supreme Commander (effectively Total Annilation with an actual storyline and updated for the current age of computers).
I'm tempted to put World in Conflict to, but although its a great RTS, I don't think its one of THE Greats.
TBS -
Civ 4 - the latest version of the classic series.
RPG -
Neverwinter nights 2 - great game, shame about the bugs.
RPG/FPS -
GTA San Andrea's - I'll admit the graphics are awful, but the plot and fun factor are too great.
Deus Ex - Need I say more? (Deus Ex 2 was good, but not great compared to its 'daddy').
FPS -
Team Fortress 2
Half Life 2 (and all its short length offspring)
Crysis (and yet I hate Far Cry... odd, I know)
Puzzle solving -
Portal (!)
Humour -
Portal - btw, it is possible to get that song from the end credits out

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For Queen and country, old clap....
Ok, I don't really talk like that, but I had you going, no?