I like chess.
I played in a few tournaments when I was 11,12,13.
I haven't played a game in years now though.
I bought a chess computer a while back, with 24 levels. Eventually I worked out a (really dumb) combination of moves that beat the computer every time at every level. I wish I could remember the combination so I can dig it out from the shed and kick its butt again.
I think chess is a fairly suitable game for autistic people. It's not easy to explain why, but my hunch is that the sorts of cognitive problems that autistic people have are not the sort that would make chess more difficult.
I think the sorts of situations where information processing causes problems for autistic people would be situations like working on a trading desk, working in a bar and large social gatherings. These are situations where you are constantly being bombarded with information that you have to respond to immediately or commit to short term memory - and if you don't do either of these things, then the information passes you by. But chess is different. With chess the information is there in front of you: you can stare at it as long as you want to, and you can take as long as you want to make your decisions. (Ok, most games are timed, but you are still given a fair bit of time.)
(And chess is obviously different to social gatherings in that with chess you are dealing with information that is discrete, concrete, impersonal etc.)
I guess chess is about spatial intelligence, and spacial intelligence is something some autistic people use to their advantage, like Temple Grandin. I might mention the autistic artist Stephen Wiltshire too, but I'm not sure if having a photographic memory is really all that similar to being able to visualise a chess board 20 moves down the line. Maybe it is; perhaps a psychologist could help with that one.
Btw, there is a thread in the Games forum about Bobby Fischer, and whether or not he was an aspie.