There are three IP ranges that are reserved for networks which do not directly access the Internet. If you use one of these private ranges, you can expand your network without worrying about running out of public IP addresses. However, by using Network Address Translation (NAT), which translates a private IP address to a public one, computers with IPs in these ranges can still access the Internet.
The ranges are:
10.0.0.0 - 10.255.255.255
172.16.0.0 - 172.31.255.255
192.168.0.0 - 192.168.255.255
All networks connecting through broadband will have private addresses, with NAT taking place on the broadband grid. If you have an ISDN connection, you may have private addresses, in which case NAT will be performed on your router.