This may affect more than one version of Windows, but I've only noticed it after a good long while with XP.
Normally I get pissed at the computer and just reboot, since I don't have the time to sit here and figure it out.
Today, I got pissed off enough to sit here for an hour or two and solve it.
Alot of solutions online revolve around the remote desktop feature and how it fails to release clipboard handles. If you have been using remote desktop recently and see either "rdclip.exe" (on the remote desktop server) or "mstsc.exe" (on the remote desktop client) tasks in your process list, simply kill them off and test your copy/pasta clipboard.
If your problem with the clipboard doesnt seem to be related to the remote desktop, then just try killing "explorer.exe" in your task manager.
Its ok, you may lose a few icons in the taskbar, or the taskbar altogether, but just run click "File" -> "New Task" and type in "explorer.exe" to bring everything back.
Now your copy paste should work again. It did for me at least. I must admit I still don't know why this happens.
