It is the IPv4 addresses that are getting close to running out, though I have no idea how to find the exact tally. Remember way back when they thought they would never run out of those? Well multiply the number of IPv4 by an ungodly number for the total IPv6 IPs available. It will be a long time me thinks, but that’s what they said about IPv4. hmmm…
IANA has announced the official exhaustion of the public IPv4 address ranges on Feb 03, 2011… There are still IPv4 Addresses available, but they have all been allocated to their respective regions..
IPv6 has a total of 340,282,366,920,938,463,463,374,607,431,768,211,456 addresses, which is currently being divided up where the las 64 bits (18446744073709551616 worth of addresses) are for hosts and the rest are for networks/subnets.
Typically, an organization will be given a /48 which gives them 65536 /64′s to play with..