I don't think it is possible to get client IP address purely in JavaScript.
If you are fine wtih some code in server side, you can try having a hidden field in the ASPX page, and assign
Request.UserHostAddress to that hidden field. Now, in javascript you can use getelementbyid of the hidden variable.
[Update after OP's comment]
In original question you said User's IP. Anyway, if it ASP.Net application, you can't find user's IP Address only through JavaScript. For Server (where you code is hosted i.e. your machine) IP address, you can check
http://stackoverflow.com/questions/1345676/how-to-get-the-server-ip-address[
^]
Hoep that helps.
Milind