The IPv4 addresses began to be distributed approximately 40 years ago. Today, they're essentially gone.This incumbent arrangement to identify the computers on the network by a sequence of 4 bytes (usually written as four.integers.below.256) may distinguish about 256^4=16^8=2^32 i.e. over 4 billion hosts which would be considered a large number of computers in the 1970s. Well, it's not too large today: in fact, it's smaller than the world population.
As recently as yesterday, the global Internet had 7/256 (fraction) of the IP addresses available. However, as expected, the Asian distributor of the IP addresses received 2/256 (fraction) of addresses from the global distributor today. This means that only 5/256 (fraction) of addresses were remaining. And there's a rule that once this happens, each continental supervisor receives one of the five remaining ones. In other words, the IP addresses have been depleted at the continental level.
For a few months, the continental distributors will be capable to spread the remaining IP addresses they have been assigned: there are not too many. On 8th of June, 2011, the leading Internet companies will celebrate the World IPv6 Day during which they will try to launch all services in IPv6 and encourage the users to access the Internet via IPv6.
Today, the percentage of traffic using the new IPv6 format is about 1 percent.
The depletion of the IP addresses is no disaster, of course. The Internet won't collapse. The limitations may be circumvented by many tricks. However, the Internet cannot grow in the simple old way. Instead of forcing the companies to use dozens of assorted tricks to circumvent the limitations on the number of available IP addresses, it seems easier to ultimately switch to a new system that gives us much more room for breathing.
The IPv6 addresses are viewed as the canonical replacement of IPv4. Instead of 2^32 hosts, they may distinguish 2^128 hosts = 3 x 10^{38} gadgets. That's approximately equal to the mass of the Solar System in micrograms, so if you convert the Sun - and the rest of the Solar System - to devices connected to the Internet and each of them will weigh at least one microgram, you will have enough IP addresses. ;-)
So if you use an IP address to identify each baguette you buy in the supermarket, the seller must be careful to recycle most of the IP addresses once the baguette is eaten - otherwise we could run out of the IPv6 addresses, too. If a new IPv6 address were used for every "event", 10^{38} would still be enough to cover the life of the civilization until the death of the Sun but it would not be too many, especially because IPv6 is built with the expectation that by generous clustering, the system may waste a vast majority of the available numbers.
Physics intermezzo
The large number 2^128 of IP addresses has already been attacked by the World Union of Kooks and Crackpots. Mr John Horgan said that such a large number was "ironic science" because you may never falsify the statement that another person has an IPv6 address: to do so, you would have to try 2^128 IP addresses one by one (at least Mr Horgan isn't capable to think of another strategy) which is impossible.
Mr John Horgan and Mr Lee Smolin have criticized the landscape of IP possibilities because it undermines the moral values. Having a large number of IP addresses is as immoral as as speculation in subprime mortgages, as Mr John Horgan figured out. You may always kill someone if you have an IPv6 address because there exists another copy of you with a different IPv6 address who hasn't killed anyone.
These criticisms by Mr John Horgan and Mr Lee Smolin, directed against the new book by Brian Greene, were not joined by their colleague in vitriol, Mr Peter Woit, because the latter is employed as a dirt eater by compassionate Brian Greene himself.
But back to the IPv4/6 addresses
The addresses will get exhausted in a few months and the pressure to open the new living space will be increasing. Most of the key Internet companies will be ready. However, many other companies and regular users may be partly screwed because they may need new routers to deal with IPv6 etc. The transition to IPv6 won't necessarily be problem-free. In fact, I am confident that the number of problems will be vastly higher than what we saw during the overhyped "Y2K problems" in the year 2000.
So several World IPv6 days may be needed to see that a vast majority of the Internet - and especially the key services - will be able to deal with IPv6.
I guess that it will be impossible to turn IPv4 off as early as in 2011, for example. The IPv6 Internet will exist simultaneously with the old one for some time. New IPv6 users without IPv4 won't be able to access services that only have the old IPv4 and vice versa (the opposite case is unlikely because there is no reason for important services to suddenly abandon the support for IPv4).
