I always liked this way of working since first touching Mathematica; does it exist for other languages? (I think there already was one for Python before, not browser based?)
[1] http://mathics.org/ [2] http://www.mathics.net/
Disclaimer, I'm the Mathics vice developer.
[1] http://ipython.org/ipython-doc/dev/interactive/htmlnotebook
Wakari is much more than just "IPython notebook in the cloud"; however, we do have great support for it. For instance, we have just recently enabled a feature which lets you host & share your IPython notebooks: http://continuum.io/blog/ipython-notebook-sharing-in-wakari
Right now Wakari is in closed beta, meaning you have to register and we manually approve accounts (which we do very quickly).