Hah this happens (used to happen) with me all the time when I was in university a short while ago. Don't rejoice because this is going to come back to haunt you. Here's why:
Our dorms had to share the internet connection from a single router. The IP addresses were sequential, like: XXX.XX.XXX.81 ... 82 ... 83 and so on. If someone got an iPhone or iPod touch, they would assign a random dedicated IP from their wireless routers and it would clash with the real owner's computer. So if whoever was using your IP reenters your wireless reach and turns his device on and assigns it your IP
when you're not using it, you get screwed again. Its extremely annoying, specially since there is no way to know who is using it. The MAC address doesn't really help.
So a little fix for everyone using a wireless router:
First make sure that someone else in your surrounding is not using a wireless device with your IP address. The next step would be to create your own range of IP addresses. This can be done in the Airport Utility application in ~/Applications/Utilities.
Under TCP/IP, under Internet enter the IP, SM, Router and DNS addresses that your internet service provider has assigned you. Then under DHCP, create a desired range of IP addresses that start from 192.168.1.1. The DHCP End Address is the number of IP addresses you want for yourself. It can be anything till 255. You can keep it till 10 or 20 or whatever, depending on the number of devices you have and can always change it. Update your router and done.
Now, automatically, your router becomes 192.168.1.1, your computer becomes 192.168.1.2, your iPhone becomes 192.168.1.3, your pet cat's netbook becomes 192.168.1.4 and so on. No one gets to take your IP because its a closed range.
Worked beautifully for me ever since I did this.