Couple of choices.
There is a simple web browser called 'linksboks' that you can run like any other xbe app. Its designed to be used by a controller. I'll save you the hair pulling and tell you that you can access the text entry by pushing in the left stick button. Its got a funky text entry system. Basically groups of 4 letters differnt colours based on the xbox buttons. You use the joystick to navigate to a particular group and 1 of 4 buttons to chose a letter. Surprisingly quick once you get used to it.
Boot into a linux distro and use firefox/opera.
If you just want something nice and simple you can run quickly without formatting your drive try 'Knoppix'. Its small and setup with a web browser / vncviewer /pdf viewer plus more ready to go. You can use a controller but a mouse makes things a lot easier.
You can find 'linksboks' in the usual place. Knoppix just google for it. xdsl (Xbox port of damn small linux) is worth a look too.
Hope that helps. Remember you xbox only has a small amount of memory comparable to that of modern mobile phones so be patient with it as little memory to buffer the webpages..
If you want to be really sick you can get win98 to run on the xbox and use ie