[stefanu]

You can try IPython (shell) and IPython Notebook (web interface) online with Wakari at https://www.wakari.io - platform (with all popular Python scientific libraries installed) that lets you run multiple Python sessions and access them online anywhere. It also allows IPython Notebook sharing - you can share your workflow.

[jpratt]

There's NBCloud (http://notebookcloud.appspot.com) if you want to host notebooks on your own Amazon cluster (great for using the parallel computing features).

Also, PiCloud (http://www.picloud.com) has a notebooks tab for launching an IPython Notebook as a job. That's useful because it means you can use their compute and data facilities with it easily.