If you have been hearing about Jupyter (formerly iPython) and have not tried it out, here are a couple quick, free, and easy options for giving it a try. No installation need, and no account setup. Just visit a link.
Easy Jupyter Notebook
Try Jupyter and tmpnb are two projects for instantly getting a jupyter notebook with just a simple URL. Tmpnb was created by Rackspace for Nature and Try Jupyter is a demo from the main Jupyter website. I believe both projects use the same open source code found on GitHub. They might even be 2 URLs to the same infrastructure.
The major limitation is the lack of an ability to comeback to your notebook later (which is not a problem if you host the Jupyter notebook on your own). The notebooks die after some time of inactivity, but you can always create a new one. For more on the design decisions, see the Rackspace blog post, How did we serve more than 20,000 IPython notebooks for Nature readers? or join the open source project on GitHub.
If you have been wishing to try our Jupyter, it cannot get much easier than these options.