I've got several Add-ons:
1-click Weather, ColorfulTabs, Download Panel,
Download Statusbar, DownThemAll, Duplicate Tab,
Firefox Showcase, Flashblock, gui:config,
No Squint, NoScript, PopupMaster,
QuickNote, Read it Later, Searchbar Autosizer,
Site Launcher, Tabs Open Relative, User Agent Switcher,
I now strongly suspect 'Site Launcher' is the culprit, which I'd forgotten
about. It will open a site with the key combinations Ctrl-Shft-[a..z]. In
particular Ctrl-Shft-f will open Facebook and Ctrl-Shft-d will open Digg,
whatever that is.
I've never intentionally used it, and have now uninstalled it. I can't even
recall now why I thought it was a good idea to install it in the first place.
Sorry for the dumb question.