I'm among the many afflicted after an iOS 6 upgrade on my iPad. Issue continues after 6.0.1.
Specifically, the sound randomly stops working - as though the whole sound system has crashed. It is independent of the use of headphones, and I don't have a dock. Volume buttons still produce the volume feedback overlay and move up and down accordingly, but nothing produces any sounds - no alarms nor notices, and if I attempt to play anything via the Music app the play button, after initally changing to the double-bar "pause" icon, reverts back to the "play" icon after about half a second (and there is no progress on the song).
I do not have a dock to test against, nor have I ever used this with a dock. Plugging headphones in does nothing - music still won't play, audio still won't sound (so it's not a hardware issue with the interior contact switch). This happens whether or not "Do Not Disturb" is ever used, or the scheduled DND notification suppression is on - tried it both ways to be sure.
The only resolution I have found is to power-cycle the device: "slide to power off", let it shut down, power it back up, and then all sounds work correctly again.
The onset is apparently random, sometimes 2 days on a row, sometimes it can be 2 weeks between occurrances. This never happened to me with iOS 5.x, and only started after the 6.0 upgrade (and first happened within a day of the upgrade).
I used to rely on my iPad as an alarm clock, but this unreliability has been extremely frustrating.
iPad 2 (Model MC916LL)
iOS 6.0.1 (10A523), but it started on 6.0