This tip is useful for Windows Server Administrators because, by default, Windows Server does not have the "Personalization" Control Panel that is immediately available in Windows 7. Rather than install the necessary additional Features to Windows Server to make it possible to perform the remove of the icon - it is easier to hack the registry.
The following will hide the Recycle Bin from the Desktop in Windows Server 2008 R2 (also works for Windows 7)
Windows Registry Editor Version 5.00
[HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\HideDesktopIcons\ClassicStartMenu]
"{645FF040-5081-101B-9F08-00AA002F954E}"=dword:00000001[HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\HideDesktopIcons\NewStartPanel]
"{645FF040-5081-101B-9F08-00AA002F954E}"=dword:00000001
