well I think that this type of thing coming about isn't going to be because of a super computer, but lots of computers creating/solving and storing the various tablebases - where individual positions are solved out to mate, or a forced draw.
For example, checkers has been solved. A very weak computer can play "perfect" checkers, just as long as it can access this data. It is not thinking or calculating, just looking up positions, where it can find the best move.
http://en.wikipedia.org/wiki/Endgame_tablebase has some interesting information about it.
I recently installed all of the 3,4, and 5 man tablebases, and it is very nice for doing analysis of endgames. I believe that all of the 6 men tablebases have been solved as well, and quite a few of the 7 man tablebases.
Once we have a 32 man tablebase, chess will be solved :-)