There's some cleanup to be done on the IPython side, but this shows two simple apps backed by an IPython Kernel (requires IPython ≥ 1.0).
Start the app with
The first is a single IPython code cell - this is the most complicated, with the most dependencies, because the CodeCell object is actually where most of the IPython Notebook's complexity lies - it brings in CodeMirror, completion, the tooltip, and other things, all of which are not optional. Some of this needs to be cleaned up.
The other demo is a plain webapp - no IPython input cell or anything, backed by a kernel, where moving some sliders result in recomputation of plot data, which is sent to the frontend and plotted with flot.