1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 possible bitcoin addresses.
As ribuck says, that is a very big number. There are approximately:
133,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
.. atoms in the Earth, so even if you used just 100 atoms to store each bitcoin address, you'd run out of atoms before you were done generating addresses.
Cool abstraction!