For me, Project Gipf really takes the cake -- 7 tightly designed games that play on small hexagonal grids, with interesting and unique mechanics. Play time is short. Simple games with profound depth.
I am also a sucker for Havannah -- very simple connection game with a lot of depth -- and Hive, a bug-themed game where your soldiers are hex tiles that make up the board. (a bit like chess)
For less abstract games, my favorite classic game, which I frequently wager stakes on, has to be backgammon -- despite the dice rolling, simple-yet-deep game. Fun to play at the bar and with family.
Another one I love is sittuyin. It's a chess variant closer to ancient chess but where you can choose the position of all your pieces at the beginning.