About a decode ago a computer finally beat the best chess mind on the planet. Computers can play nearly every game we've invented better than us. However, one game stands out as unbeaten. The ancient Chinese game of Go. The Times of London has an interesting article on why the computer still can't beat an average human Go player.
The computer can play chess because it can calculate the results of all possible moves and then pick the best one. In chess, there are usually 25-35 possible moves at any point. In Go, there are 250. This makes the brute force strategy a lot harder. Almost impossibly hard. The thinking goes that playing Go well is all about recognizing patterns--something computers are notoriously bad at. If so, being able to play Go well would be a breakthrough affecting lots of other areas of computing from vision to AI.
This reminds me, I still have to find the time to learn to play Go. It's one game I've never played yet.