If you're using a router of some kind, you can just set a static IP as suggested. Depending on the router, you might be able to set up a static DHCP list, and make life a little easier.
If you're directly connected to the Internet however, then you're kind of stuck. Almost every ISP uses some form of dynamic IP system, unless you pay for a static IP. So every time you connect to the Internet, you're likely to get a new IP, or after a set period of time (which is different for every ISP) your IP will "time out" and you'll automatically be assigned a new one. You can't just go assigning yourself an IP address in cases like this. If your ISP's systems don't stop you from doing it, sooner or later it'll cause problems for other people, and when your ISP investigates it won't be very hard to track the source to you.