And, to add to the above, the list of possible "private" IP addresses:

10.0.0.0 - 10.255.255.255
172.16.0.0 - 172.31.255.255
192.168.0.0 - 192.168.255.255

Although, technically, one part of frog's post isn't quite correct......you CAN have a different IP address on your computer to the one on your router, with your computer NOT being on a private IP address......my router's IP address is one public IP, my computer is on another (different) public IP address, and the router dishes out one of the 4 remaining public IP addresses in my block of 8 to any other machines that connect to my network......but that's just complicating matters and me being pedantic!