There are many services that do this but looking in the Debian distributions package change logs I noticed that they are using http://checkip.dyndns.org/ to return your globally recognized IP address.
And it returns a very nice sparse reply as follows.
<html> <head> <title>Current IP Check</title> </head> <body>Current IP Address: 220.127.116.11</body> </html>
So using a simple script you can parse the html and get the IP out for your own needs.
It seems many of the other websites that return your IP address have about 500KB of adds on the page. So this is definitely a winner.