It's a good idea to remove unused icons from your desktop, as it does eat up resources (RAM) when your screen is full. It's also better for productivity to have a well-organized Start Menu (or folders of icons on the desktop), instead of a massive blob of icons barfed randomly all over your desktop.
For me, the Libraries shortcut is worthless, and just takes up screen real estate.
Removing it is easy. 
To remove the icon/shortcut, quickly perform the following steps:
Step 1. Go to the Registry Editor (regedit).
- Don't know what/where that is? You open it by clicking Start, go to Run, type in "regedit", and click OK (or hit Enter)
Step 2. In regedit, go to Edit > Find, and search for
HideDesktopIcons.
- It will be found inside several subfolders, at \HKEY_CURRENT_USER\Software\Microsoft\Windows\Curr entVersion\Explorer\HideDesktopIcons\ClassicStartM enu.
Step 3. Click on
ClassicStartMenu on the left part of the screen, and then in the right half of the screen right-click and select New > DWORD (32-bit) Value. Name this value
{031E4825-7B94-4DC3-B131-E946B44C8DD5} -- and do NOT forget to include the {} characters!!
Step 4. Double-click on the name of your newly-created entry, and change the
Value data to
1. OK and close regedit.
Step 5. Click on an empty spot on your desktop background, and then press F5 to reload the desktop. (Or right-click with the mouse, and select Refresh.) The Libraries icon/shortcut should now be gone.
Sample image:
Registry Editor_2012-08-01_10-08-23.jpg
Done.
