-The OS will read more RAM (which you don't need yet...but soon enough)
-The 64-bit processing power if you have a 64-bit CPU. Right now you may not see a big difference in gaming but perhaps one day).
-You'll be OS proof for the future.
However, be reading to run into some compatibility issues sometimes. You can usually solve the problem by running the 32-bit version of the game if the 64-bit doesn't work.