Sound Settings is missing all output devices

Turns out I was running into Bug #590780: Installing "randomsound" package causes Pulseaudio to stop functioning at reboot and didn't know it yet. See this answer:

1. Run pstree | less
2. In that, type /arecord and press return to find the arecord process.
3. Press up once and you'll see its parent. In my case this was randomsound.