I'm referring to the menu I get when I right-click on a layer in the TOC. I'd like to move Properties to the top. I can't find anything in the customization dialog that seems to apply.
I haven't found how to re-arrange those items, but most of the items in that list can be assigned a shortcut key through Settings -> Configure shortcuts... as an interim option:
You could make a feature request for the ability to re-arrange context menus at http://hub.qgis.org/projects/quantum-gis/issues