Also http://whatismyip.akamai.com/ for a completely clean "get my IP" page
Some applications need to use the public IP address. So far we mostly have to maintain our own solutions (http://myip.wampdeveloper.com/) for our own products (http://www.devside.net/server/webdeveloper).
I got excited about GoogGoogle's IP query, then I looked at the page's source code! I guess I could parse that but still, there is no guarantee the format/syntax/text would stay the same.
So far I've seen a few dozen different IP return URLs. And I'm sure there are 1000s more private ones. If we could have one that's guaranteed to be around, that would help everyone out.