Suppose I should make a comment on my number #1 pick.
I think it would be fair to say that, with the exception of maybe The Sims, Counter-Strike was probably the most impactful on the industry out of all the games released in 2000. It was a pioneer in competitive asymmetrical multiplayer, something that we're still seeing innovation in today, and the first example I can think of of a mod that was acquired by the original games developer and turned into its own fully fledged game.
Every popular first person shooter has now copied its formula of bomb defusal, 1 life, game type. It was the Battle Royale of the noughties, at least until Call of Duty 4 changed the industry yet again in 2007.
I didn't discover Counter Strike until 2003/2004 when me and my friend began exploring PC gaming. I loved the fact that you could learn a predictable spray pattern, rather than the twitch shooting of Quake and Unreal. Learning the maps, player movement, throwing smokes in JUST the right place. Not picking up your weapons on the map but buying them with money you earn by playing well!
I'm just gushing at this point, but seriously, and incredible, innovative game that changed the face of first person shooters forever. I haven't even talked about the mod support, zombies, surfing, etc. If you've never played Counter Strike, pick up Global Offensive when it's on sale.