This application implements a mostly-complete X11 server, running natively in Android. It allows X Window System applications to be run remotely and displayed on an Android device with internet access.
Note that this application does not come with a window manager. However, it is possible to run a window manager remotely, which is fiddly but seems to work.
This is still a beta release, so feel free to report any bugs you find, or, better yet, fix them yourself. Yes, it's open source, hosted at http://code.google.com/p/android-xserver/
Added the XTEST extension.