In My Computer or Windows Explorer, go to c:\users\<your user name>\desktop folder. Rightclick in the right pane and choose view>detail. Do you see two of each? Can you delete the duplicate?
If it looks good there, try a reboot. Might help.
I was pinning some shortcuts to the task bar and removing these shortcuts from the desktop. Somehow I ended up with duplicate shortcuts and icons for each one that was originally on the computer desktop (even those I was not moving). These duplicates are not useable - they cannot be right clicked; they do not highlight when hovered over.
I am running Windows 7 on a Dell Vostro 1720 laptop.