There have been requests for web browsers on Raspbian to fill out the GUI experience. I've looked into it and at a minimum we won't have one for at least another 4 days or so. The reason is that Midori and Chromium both rely on webkit which according to the Debian armhf build logs is an 81 hour build on similar type of hardware we are using to build Raspbian. Gulp!!! 81 hours!!! That's a 3+ day build...
Even worse, it looks like they both rely on different versions of webkit. Firefox/IceWeasel even a separate huge build. No matter what, these are going to be very painful builds to get through and we'll have to exercise patience. I don't have knowledge of how to cross-compile such complex Debian packages so there isn't much of option to use more powerful Intel hardware for these builds (which isn't the Debian way anyway).
To get through this as quickly as possible, I've stopped autobuilding on one server and devoted it to building webkit for the next 3+ days. I had to use a handful of Debian armhf packages to satisfy build dependencies so there is a risk that at the end of these builds we can't use the packages as they may have ARMv7 contamination and won't run on the Raspberry Pi. However, this risk is generally pretty low so it's probably worth taking to these critical pieces of a GUI experience built.
Since the build system I do manual builds on will be devoted to webkit for the next few days this will give me time to turn my attention to fixing up the Raspbian.org website and some infrastructure issues I've been meaning to get to for the last week or so. Plugwash has been busy with his own set of manual builds on another build server so we'll have three to four other autobuilders pounding on the scheduled set of packages. Binary packages will be coming out slower for a little while, but they progress will continue to be made.
PS. If you want to go old school, you can use the lynx browser on Raspbian which is a text-mode browser. Doing so, at least you'll really appreciate Midori or Chromium when they do show up on Raspbian.