Today, the ICANN (Internet Corporation for Assigned Names and Numbers) has released the last batch of IPv4 addresses. So today is marked as a Milestone in the Internet History. The beginning of the end of IPv4 - which is expected to definitely happen in 2012 (Update: In fact, major Internet service providers (ISPs), home networking equipment manufacturers, and web companies around the world united to redefine the global Internet and permanently enable IPv6 for their products and services on 6 June 2012 worldipv6launch.org)
IPv4 addresses are the addresses we commonly know and used nowadays (e.g. 192.168.100.51 255.255.255.0) which are 32-bit addresses and can span a maximum of 4.3 billion addresses, which are apparently running out fast, very fast...
The alternative is IPv6 addressing scheme where a 128-bit-address is used to address a machine. Which obviously spans a larger number of addresses (more than 340 undecillion, i.e. 340 billion billion billion addresses) which should be sufficient for a very very long time. This scheme also uses the hexadecimal notation. (e.g. fe80::21f:3cff:fe5c:1b39/64)
Most of our home computers with modern devices and operating systems, support IPv6. The only change is at the internet providers level, and some enterprises, where they need to upgrade the hardware to support the new scheme.
To check your current IPv4 and IPv6 settings:
Using the "ipconfig /all" tool in the Command Prompt
*UPDATE: Capture on Windows 7 OS
An Interesting review of the issue is available from CNET here