Blokus is a board game that is superficially related to Tetris. You have a square board and the idea is that you place coloured shapes onto the board, your pieces can only touch on their corners, and as the 4 players each place their pieces on the board you start having to think about how you can get your pieces to fit in the gaps left by their pieces. Each game takes about 20 minutes to play and my kids (10 and 7) enjoy playing it with their mum and dad.
On the surface it's a simple place the pieces game, but given that there are 3 other people playing it can become quite tactical. I've played it with most of the people I know and it kept several people (ages 10 to 80) occupied on a new years day. You can even play some single player game variations on the game.
The biggest problem is that you need 4 people to play a game, but it does make an excellent family game.
Just a very late addition to my review - you can indeed play with 2 or 3 players quite happily. Playing with three generates a very strange set of strategy as each of the three players takes turns playing the remaining colour on its go (it works really well), but I do find the two player version, where each player plays two colours, the least satisfying. After several months it still gets a regular dust off as it's just good fun.