To do this, I went to Synaptic and added nautilus-actions. The Nautilus Actions Configuration Tool shows up in the main menu under System > Preferences. Here's the main window:
To add an entry to the desktop's right-click menu, first click on the "Define a new action" button, or use File > New action. On the Action tab, put check marks in the "Display item in selection context menu" and "Display item in location context menu" boxes. Next, type something in for the Context label. You can also browse for an icon for the action on this tab.
On the Command tab, you can add a Profile label, and indicate the command to be used.
On the Advanced conditions tab, add a scheme called "x-nautilus-desktop." I think it needs to be the only scheme selected.
Go to Edit > Preferences > Runtime preferences tab to configure the ordering of the items:
At this point, you can save your changes. You may or may not have to restart GNOME. Use the same procedure to add more entries to the right-click menu.
I haven't found a way to add GNOME's main menu to the desktop's right-click menu, but I found something very close. I went to Synaptic and added gnome-main-menu, then used the command /usr/lib/gnome-main-menu/application-browser in the Nautilus Actions Configuration tool to add an entry for the Application Browser, which looks like this:
That's a pretty good tool, although not quite as good as GNOME's main menu, in my opinion.
