WyeSoft

http://ip.wyesoft.com/download.html

My latest application, testing internet connectivity with wxLua. Very simple - just tells you your IP address and copies it to the clipboard with one click. It's completely portable too - no installation necessary.

The web page that displays your IP is still there, but the application is quicker once you've downloaded it. I recommend it if you have to check your IP address regularly for any reason.