http://www.netsurf-browser.org/ Raspieman got this working on Raspberry PI
Small as a mouse, fast as a cheetah and available for free. NetSurf is a multi-platform web browser for RISC OS, UNIX-like platforms (including Linux), Mac OS X, and more.
Whether you want to check your webmail, read the news or post to discussion forums, NetSurf is your lightweight gateway to the world wide web. Actively developed, NetSurf is continually evolving and improving.
Midori (緑, Japanese for green) is a web browser that aims to be lightweight and fast. It uses the WebKit rendering engine and the GTK+ 2 or GTK+ 3 interface
Lightweight browser that works with the Raspberry PI