You should keep as many as you want to make your feel protected.
For me, it's about a month worth of backups.
Well, I just deleted 396 folders, worth about 114G of hard drive space... it felt so liberating!
Let me ask a question based on your screen capture
Are the Backups stored under "Pictures"? That doesn't seem to be the proper place for backups.
Backups must be on a different disk than the original catalog file. You can't have them on the same disk as the catalog file. If you have your backups on the same disk as your catalog file, then you'd need to change the location of the backups to a different disk.
You also need to be making backups of your photos separately (Lightroom does not do this)
I have two separate Time Machine external hard drives and Crash Plan cloud back-up, so I hope I'm covered!
Ok, that's fine!