I've never played with one but I have read studies on them in relation to our unconscious mind.
I play chess but I'm terrible. I never spent that much time learning so I'm sure that is the issue.
I've played Risk online and always had a good time.
My wife and I play Scrabble. It causes many arguments and is the only time in my house that the dictionary gets dragged out.
I love Monopoly. I usually do pretty good but upset the people I play with.
I play a game called Czar which is pretty good for a two player strategy game.
http://en.wikipedia.org/wiki/TZAAR
I also play Dvonn.
http://en.wikipedia.org/wiki/DVONN
They were all released as part of a series.
http://en.wikipedia.org/wiki/GIPF_project