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.
You can create a custom report type of the report object that will include the report type as a field - then create a report using this custom report type. This report will be able to list the report types of all the reports.
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 ;)