Depends on your setup. If you have dialup, or cable/dsl without a router then yea it will most likely change everytime you reboot. Everytime you dial out for dialup connections. If you have a router, you will probably not see the IP change. But with a router that isn't the IP you need to use to allow people on the internet to play on your computer, the right IP will be listed in the router configuration screens somewhere.
See
The Big Lan Book for more info.