I use the ipython notebook sometimes, but I almost always use something similar. (In my case, I often use emacs org-mode files to make basic literate program-style documents.)

I keep these things in a dated "Notebook" file, like "Notebook/2013-07", just to hold all my one-offs.

Why do I keep them? Well, often it takes a while for me to set up the particular environment I need. If there's a problem with the calculation for X, I need to load the right data, set up the context for X, run through the individual bits until I see what the issue is.

I save the ipython notebook where I go through all that, and then if I need to go back to the calculation, for example to demonstrate to someone else my example that something has gone wrong, then I can just load up the notebook. If something is supposed to have been fixed, I can load up the notebook and repeat the calculation and see if it works now.

Unlike emacs org-mode, I can easily save the graphs as part of this. ("Look, if I plot the distribution, there's this big extra lump over there. Where's that coming from?")

If I go back to a file, it typically takes me a bit of thought to remember exactly what I was doing there. Once I figure it out again, I add sentence or two of markdown.

It's a useful thing to have around.