A few weeks ago, my wife and I managed our first quick game of Blokus - bought as part of my current drive to acquire simple games that I can play while nearly brain-dead after a hard day's work. It's not a bad game at all, and runs something a little like this:
1. the players take it in turns to place tetris-style shapes onto a grid;
2. starting in a corner and working inwards;
3. each player using shapes of one colour (except in the two-player game, where you take two colours);
4. each shape of a given colour must touch corner-on to another shape of that colour;
5. each shape of a given colour may ONLY touch corner-on to other shapes of that colour, but may touch shapes of other colours without restriction;
6. the game ends when no colour can place another shape;
7. you lose one point for each square you still have unplaced (so 4 points for a shape made up of 4 squares), gain 15 points if you've placed all your shapes and an additional 5 points if you finish by placing your 1-square piece.
We enjoyed it - having played a few more games since with two and four players, I've started to get a feel for the strategic aspect and for how easily you can find your moves curtailed if you're not paying attention. Two much-less-boardgamey friends have also played it with us and enjoyed in particular the discrete cut-throat aspect of the game, where you try to block another player in without making it obvious that you're blocking him in and thus triggering horrible reprisals or fits of sulking.
The game allows nicely for a certain amount of cunning but, crucially, can also be played just for the social experience of doing something more interactive than watching telly.