How many IP addresses does IPv6 support? Well, without knowing the exact implementation details, we can get a rough estimate based on the fact that it uses 128 bits. So 2 to the power of 128 ends up being 340,282,366,920,938,000,000,000,000,000,000,000,000 unique IP addresses.
Well, we know that sounds like a lot, but this blurb from http://en.wikipedia.org/wiki/Ipv6 really puts it in perspective:
"approximately 5×1028 addresses for each of the roughly 6.5 billion people alive today. In a different perspective, this is 252 addresses for every star in the known universe – a million times as many addresses per star than IPv4 supported for our single planet"