A place I learned about several new board games was on Geek & Sundry's YouTube channel. Wil Weaton does a show called TableTop . They show off playing table top games and you can obverse how they play before actually purchasing them. I've ended up buying several of the games they have played (and enjoyed playing them with friends and family).
I've really enjoyed several cooperative games (Pandemic, Forbidden Island, etc). Games where either everyone works together and wins or everyone looses.
Ticket to Ride is another fun one. Relatively simple game play, but requires a lot of strategy (and luck).