Puerto Rico. This is actually may well be Roman’s favorite game of all time so he’ll write first person from here.  I once finished second in a GenCon tournament of 50-60 people, and I still play online.  I prefer the original game to the expanded version, though I prefer the balanced rules to the original rules.

This game doesn’t have a ton of do-something ability nor is it especially thematic so it sort of goes against the grain of what I like, but it’s highly strategic and I just get into this one.  A Euro-style game where each player chooses a role each turn.  One of the few games with no dice and no cards and very little randomness, yet can be played again and again.