Settlers of Catan.  I'm not sure if it really qualifies as a board game, but it's close enough for me.  Instead of your classic "board" it has tiles of land/water that you build cities and settlements upon.  The person who reaches 10 points (or if two people and a good game - 15 points) wins.  You never have the same layout twice due to a shuffling of tiles and I think that's the biggest draw for me.  Rather simple and lots of fun.  It can even be found online.

Hilarious story - I had brought my game to the FS I used to work at.  We were playing a good game when we commented that G must really like sheep.  She replied back that she preferred cows and was into "moonagamy".  I suppose you had to have been there.