Originally Posted by Bratwurst

Your IP address doesn't change most likely because your router hasn't had to ask for a new one from the DHCP server. If you unplugged your cable/dsl modem for a bit, or say you lost power for a few hours and your DHCP lease had expired, you may get a different address. It just depends if someone else made a request to the DHCP server while your modem was offline and it served them your old IP address. Since you rarely ever drop your connection, your IP address will rarely change. But the possibility does exist.

So if you want to run a server at home that requires a static address, you need to actually order one to be absolutely sure. There are a few utilities out there though that get around this. You use them as a 3rd party host and they forward the traffic to you regardless if your IP changed.