there are 4,228,250,625 possible with the current IPv4 which is only for those computers actually connected to the internet;
remember only static ip users need these...
most isp and or host actually give you a static ip which is routed through thier own ip.
same goes for dynamic ip's ... which means there are 4billion each isp can have for thier customers routed through a single ip.
then you have the static hosts (T1/T3/etc) but again, most of these are websites on a host routed through a single IP or are a College/Uni again routed through a single IP.
IPv6 however allows for something around 72,057,594,037,927,936 possible IP address'.
anyway you look at it, doesn't really consern us as the in-charge of keeping the internet ticking over won't allow it to actually reach it's maximum... they'll always invent a higher address space.