Picked this up on a blog-

The number of distinct chess positions after White’s first move is 20 (16 pawn moves and 4 knight moves). There are 400 distinct chess positions after two moves (first move for White, followed by first move for Black). There are 5,362 distinct chess positions or 8,902 total positions after three moves (White’s second move). There are 71,852 distinct chess positions or 197,742 total positions after four moves (two moves for White and two moves for Black). There are 809,896 distinct positions or 4, 897,256 total positions after 5 moves. There are 9,132,484 distinct positions or 120,921,506 total positions after 6 moves (three moves for White and three moves for Black). The total number of chess positions after 7 moves is 3,284,294,545. The total number of chess positions is about 2x10 to the 46 power. If you understand this and like math tell us the answer.

There's a better page on wikipedia that explains it a bit better, however:

http://en.wikipedia.org/wiki/Chess#Mathematics_and_computers

So between 10^43 and 10^50 positions, given that nobody else is smart enough to figure out how to account for all the special cases and arrive at an exact number.