I want to add an item into the Desktop context menu (the menu you see when you right-click on an empty space on the Windows Desktop).
Something like Catalyst Contr
There's a series of articles on CodeProject that details writing Shell Extensions and is very good:
http://www.codeproject.com/KB/shell/shellextguide1.aspx
Such a handler must be registered in HKCR\Directory\Background, instead of usual locations like HKCR\Directory, HKCR\Folder, etc.
Check out Creating Shell Extension Handlers in MSDN.