I'm not sure if this was a mistake by the programmers by not automatically deleting previous backups but I've amassed about 10 Gigabytes for obsolete - old Lightroom catalog backups. Perhaps this is a use for having multiple backups at hand - but since I have a strong backup routine with all my other files, I think I can risk just having the last backup or simply to dump the whole backup catalog process.
So where do you find and delete these old Adobe Lightroom catalog files? In Windows its in your documents under the Photos folder then /Lightroom/Backups... So if you find yourself short of disk space (these backup catalog files/folders take up about 500 to 1 Gigabyte each!!!) you can find these folders and just delete them. While you're thinking about cleaning up your catalog, it may be a good idea to also "Optimise your catalog" to make it run faster (And defrag your computer while you're at it).