I have accumulated scores of custom reports types within my org and some of them I think are obsolete, therefore I would like to remove them, however, in the interest of integrity, I would like to make sure that no reports are based on the report type that I want to delete, therefore I am looking for a way of reporting of the reports by report type so that I can find out this information.
Fetch all reports to Force.com IDE (if you have LOADS of reports try to do it couple folders at a time - the metadata API can retrieve 5K objects in one go).
Then Ctrl+H (or any non-Eclipse "find in files" of your choice) and search for the report type API name.
Reports that use it will have line similar to
This sounds like a lot of hassle but probably you should backup the reports anyway before this purge so ;)