#2 game on BGG. I like the fact that the rules aren't actually that complex, while remaining a tactical brain burner with a little randomness and bluffing thrown in to keep it fresh. It helps that you can play it for free on BGG.
If you're into the ever shifting strategy of Risk and Settlers of Catan, you'll love Tigris & Euphrates. Four players build civilizations on a map board and collect points by keeping their leaders connected to their empires. Declare war or join 2 civilizations to boot a leader off the board and claim their territory. You keep your points hidden til the end, making it tough to calculate who's winning. One minute you're dominating the board, next you're off the map. Exciting and fun every time!
I love Reiner Knizia's games. This one is a little more involved than some of the others, but it is a wonderful Eurogame. It involves building civilizations through tile laying. In a great twist, the number of points in your weakest category at the end becomes your score.