The problem: Somehow, someway, files have been created on your drive that have a full path name that are too long for you to delete, highlighted by the following error when attempting to SHIFT-DELETE a file in Windows Explorer:
Similarly, if you try opening up a command prompt and try using rmdir /s, you'll get an error stating "The file name is too long.", or "The path xxxxxx is too long.". What's left to do? Format the drive? What if you have other important data on that volume? In my case, I was putting together a robocopy script to backup the files in my c:\user\my_username directory to a network path. In testing out all the switches, I forgot to exclude the AppData folder. When I went back to the destination and attempted to delete the AppData folder, I ran into the issue above. Somehow, inside the AppData folder, were at least 15 or more nested Application Data folders! I somehow really gorked my robocopy script, and no matter what I tried, I couldn't get that directory to go away. I tried the suggestion in the error message to no end, I would get similar errors to what is listed in the screenshot above. So here is how I fixed it.
The only requirement to using this method is that you need a partition/volume/disk/flash drive/etc that you don't mind formatting. The reason why will become apparent later. The basics of this method is to use robocopy with the /move switch. For complete documentation on robocopy run "robocopy /?" at a command prompt. In my situation, I formatted a flash drive, created a folder on it, shared that folder, then instructed robocopy to move all the data from the problematic directory to the shared folder on another computer(the computer with the problem directory didn't have a memory card reader).
robocopy d:\problematic_folder \\computer1\shared_folder_name /move /e
Afterwards I confirmed that the AppData folder which I could not delete before, was gone. Next I moved to computer1 and simply formatted the flash memory card. I have tested this locally as well, i.e.
robocopy d:\problematic_folder e:\destination_folder /move /e
Next you just format the flash drive / partition / volume / usb thumb drive / etc to clean it up.