How do I run Tomboy in the notification area at startup?

There is an undocumented option --icon that makes tomboy start without showing a window. It HAD a bug (bug #566421), which has now been resolved.

Also, you can use the tomboy applet: Right click on the panel, choose “Add to Panel” and select “Tomboy Notes“. The panel applet looks similar to the notification area icon and provides the same functionality (hotkeys and popup menu).