My main use is for web scraping + javascript support, since I love Python and I like the HTMLUnit headless browser written in Java. I've written two articles using it:
i) http://blog.databigbang.com/web-scraping-ajax-and-javascript...
ii) http://blog.databigbang.com/automated-browserless-oauth-auth...
Here's another use case. At Repustate, we have an API to create PowerPoint presentations via an API call. We use Apache POI (Java) to create & manage PowerPoint slides, but our code base is all Python. So we have a Jython process running on Jetty, but instrument all of the Java bits with Python.
It's pretty amazing to have all of the power of the JVM at your disposal but with the grace of Python.