Show My IP Address Light  

You are looking for a very light weight web application which not only shows you your ip address but has also advanced features like showing you the headers sent by your browser? Try this text based web application which needs less than 1 KB what makes it very suitable for mobile devices:

http://www.rabbitcoder.com/ip - Light version (~500 Bytes)
http://www.rabbitcoder.com/ipl - Ultra light version (~40 Bytes)

Enjoy!