This made for an interesting read... I also didn't know that there was a mandatory 75 move rule - anyone else know about that?
http://chess.stackexchange.com/questions/8331/is-the-number-of-possible-chess-games-infiniteThe 75-move rule was added in the 1st July 2014 FIDE rulebook update, along with the (in my opinion) confusingly-worded fivefold repetition rule. Both are "arbiter" draws in long games - the arbiter can intervene upon noticing the conditions are fulfilled.
Those put an upper bound on the longest game possible, and also on the positions possible (going by the standard definition of "position" as board configuration + side to move + castling/ep rights + pawn move/capture countdown + repetition number).
Personally I'm not really interested in the exact number of legal positions (a very irritating combinatorics problem, and an estimate will usually suffice for whatever purpose you have), especially since what constitutes an "illegal position" is extremely tricky to verify. There exists no program (or even reasonably implementable algorithm!) to determine if a position is illegal. That's one aspect of the field of retroanalysis, to which I'm much more partial.
It gets even worse if you consider repetition numbers that cannot have bearing on the game to be the same. (eg. if a position is not reachable in 3 moves from now, and it's been 73 moves from the last pawn push, then technically that does not change the state, in a sense)