There are two types of IP addresses for the most part, Dynamic and Static their names represent what they really are, dynamic is changing while static is non-changing. If you are on a residential connection, DSL,Cable,or Dial-up the chances you have a static IP are very low. Static IP's are more of a premium and reserved for commercial customers that need to keep their IP address the same all the time (ie Webservers). Since your IP address is a way of uniquely identifying your computer on the internet webservers and other online hosts want their IP to remain the same so that when someone types in their web address it will translate to their IP address and they can be found online. Sometimes dynamic IP's don't change often usually in the case of an always on connection.
You can tell if you have a dynamic IP easily by opening a command prompt (Click Start->run type the word command, click ok) and if you are a winxp/2000 user type ipconfig -release, hit enter your IP address will now be 0.0.0.0, now type ipconfig -renew your computer will more than likely pick up a new ip address different than the one you had before. If this does not work you can always unplug your cable modem/router for a few minutes then it should pick up a new one, if it does you have a dynamic IP.
If you have a static IP enjoy it, its a luxury on a residential connection, you can do things that lots of other people can't with it.