Windows 95/98 - open a command prompt and type "winipcfg"
Windows XP, 2000 - Goto Start menu and click "run...". Type "cmd". A command prompt will open, then type "ipconfig". This will display your IP address.
Mac OS X - Click the Apple dropdown menu and choose system preferences. Then "Internet and network" click 'network'. A window will open with your IP address in it.
If you are behind a proxy or local gateway (example: your IP shows up as 192.168.X.X), then goto a website that will detect it for you, such as Http://www.IPChicken.com
Have fun with your new info!