I want to add a few games that haven't come up yet.
Morels-Lazy 2-player competitive game
A simple little game design of set collecting that happens to be from a designer here in Pittsburgh. Good game for a late Sunday afternoon with just the wife and I.
We have also taken to playing Ticket to Ride as a two player game and it actually works surprisingly well, the strategy is totally different from 4-5 players, but it works.
If we aren't playing either of these, we play Pandemic. I tend to enjoy cooperative games for two players since playing the game kind of 'fakes' a 3rd player.
Power Grid-best competitive small group (5) game for more casual gamers
I got this one as a gift from my brother a few years back. It is excellent. Multi-faceted strategy, tension over space, sometimes epic miscalculations (I once could have won if I had only built my 17th city only able to power 14, but figured someone else would have had me beat, whoops).
Imperial 2030-best competitive small group (5) game for more serious gamers
A game that you never are actually 'out' of is always nice. While there are certainly times when you know you won't win, there are other times when you surprise even yourself with how well you did even after losing a controlling stake in a country. Something like Catan often suffers when one player has 7 VPs and another still only has 2 or 3 and it can turn into a game of sabotage which I think negatively impacts the balance of the game.
Diplomacy-best game for total nerds
Yeah, this game is awesome, and yeah it will take forever to play even a few turns, but the combination of role-playing elements and high stakes war games really works, and 6 hours in you will still feel like you want to keep playing.
That's all I've really got. I've played a lot of games, some just once or twice and have not been able to form much of an opinion on them, but an honorable mention for Shadows Over Camelot and Puerto Rico both of which I've played twice, but seem like good fun. Dominion, Carcassonne, Catan, Munchkin, Lords of Waterdeep have all been mentioned so I won't go into those other than to say I enjoy them also.
The one I own that I think I may sell is Agricola. I don't know if it is the general play mechanics or the theme, but I just can't get into it. It feels as if it ends too soon, before you really get your farmstead rolling and then you just count points, it isn't satisfying to win.