If it's your LAN IP address - the IP of your computer on your home network - then it's very likely that someone else will have that same IP. If you've got a home network, and it's based off a router using default settings, then chances are you've got an IP like 192.168.0.2 or 192.168.1.10. That's because the routers are factory configured to provide those IPs to any device you connect to them (they're ones used by the Netgear and Belkin routers I've used, other brands may differ). So for example, anyone with a Netgear router using default settings is probably using 192.168.0.n addresses. This is possible because they're only used on your home network - they're not attached to the internet. All the internet sees is the WAN IP address of your router, not your computer.
If it is your WAN IP address (the one you see when you go to www.whatismyip.com) then this could be because you have a dynamic IP address. If your ISP issues dynamic IPs (in the UK it's quite common, don't know about elsewhere) then you could easily have different IPs every time you connect; which would also mean that someone else will get your IP at some point (as you would theirs).
Those are the two most likely ways to see your IP somewhere else - does that help?