OK! I figured out what it was! It wasn't CCleaner, of course. I decided to bite the bullet and search through my registry for any/all instances of
\Desktop\CC
assuming that possibly some program is referencing a folder named "CC" on my desktop, and if the folder isn't there said program would then add it. Scanned through my registry (using the Find... command) and consistently saw that Windows Media Player was trying to use this folder.
Aha!!
So, I closed the registry and opened WMP. Guess what?? As soon as WMP opened up the CC folder magically appeared again all on its own. I looked at WMP's settings and lo-and-behold, at some point I must have created a desktop folder to hold ripped songs. I don't recall doing so, but I must have (and no one else uses this computer). Anyway, in WMP's Tools/Options/Rip Music tab, at the top, was a reference to "Rip music to this location" and there was the path with the "...\Desktop\CC" in it! So, I hit the "Browse" button to point to "My Music" folder instead. Voila! No more CC folder on the desktop upon reboot and relaunch of WMP!
Whew!! I'm glad that's over -- I was going nuts, hoping I didn't have some new virus or something.
Thanks, all, for your suggestions.
Case closed!
- - fred