The Holy Grail For Game Playing Computer
These days, after computers have mastered chess, that's playing "Go". Wired has an interesting article about a recent improvement of Go playing computer programs and an interview with the researcher that had this idea.
It is commonly believed that humans play Go using mostly complex pattern recognition - and so I was kind of disappointed that the described recent approaches did not go down this way but rather use a brute force approach similar to the one used for chess. The innovation is mostly a new way to evaluate board positions using a Monte Carlo algorithm.