Is vanitygen a problem for bitcoin? Considering the amount of users of vanitygen, and the fact that each user is generating millions/billions of  bitcoin addresses, won't we run out of bitcoin addresses soon? What would happen if we did run out?
There's no problem with running out of addresses.  The identifying part of a bitcoin address is a 160-bit hash.  160 bits gives in the range of 10^48 addresses, or roughly 1 for every atom on the planet.