Is there a website where I can use the bash shell with support for xwindows, e.g. so that I can
ssh -Y into my Linux desktop?
You can also just use tightVNC
Apparently HTML5 enables your browser to be used as a terminal, and this is available in the Chrome web-app secure-shell.
It is described in the FAQ as similar to Putty, but embedded in your browser:
This is even better than any of my previously posted solutions, any of which answered the OP.
Here is a CW list of options:
Web based SSH apps
consoleFISH is probably closest to what you are looking for
This doesn't give a great answer because it is not secure, but there is a way to access a live ubuntu session using the weblive interface.
Perhaps the software that runs this, nomachine has a solution.
Another option is to install R-studio server, on a desktop or server (binaries available for Ubuntu > 10.04 or Debian > 6).
Rstudio can be accessed at