Connected through a router / modem (that is never turned off) this changes all the time. Any one know how to capture it in the index file of a web page so I can keep up with the changes?

If you are trying to run a web server over this connection you're better off using a service like dynamic dns. Serach on Google. To capture the ip address of the client that requested a web page depends on your server side technology. In ASP you could try --

Joe