J, 97 characters.
1+1 i.~,+./"2>>(0 4 8,2 4 6,(],|:)3 3$i.9)&(e.~)&.>&.>(]<@:#"1~[:#:[:i.2^#)&.>(I.@(1&=);I.@(2&=))
I was planning to post an explanation of how this works, but that was yesterday and now I can't read this code.
The idea is we create a list of all possible winning triples (048,246,012,345,678,036,147,258), then make the powerset of the squares each player has and then intersect the two lists. If there's a match, that's the winner.
