One of the things I really enjoy doing with APSR is pulling apart databases to uncover things hidden deep in the data. Most application databases provide simple reports, but when you want to do something complex is when APSR really shines.
(Warning: This post contains some advanced Queries and Scripting, sorry :-)
Recently a client found some issues with the tagging of PipeRuns in their SPPID system, and it raised questions about how many other problems were lurking in there, and how could we find them. This is a great example where APSR should be useful.