I find that GNOME3, after some period of time, freezes completely. The cursor is the only thing that responds. I find that logging in from another machine, and issueing a kill -1 to the gnome-shell process will temporarily give me response. But after 5 or so minutes, it begins freezing/unfreezing in a cyclical fashion, and quickly returns to a completely unresponsive state.
By freezing, I mean just that. GKrellM is frozen. So are clocks, and anything else that would normally show updates.h Mouse cursor still moves, but Keyboard, mouse buttons show no responses.
Some mornings, I come back to my system, and it is frozen, so I ssh in, and there is no longer any X server running at all! I reboot the machine in that case.
Otherwise, if lightdm, gnome-session, and gnome-shell are still running, kill -1 to the head gnome-shell (use pstree -plG) will give you enough response to save any work, and then log out to start the session over.
It seems (this may be purely superstition) that running firefox accelerates the breakdown. I usually have more than a few tabs open; I have Konsole and Terminal both running with maybe 5 tabs open on Konsole, and 20 tabs open on Terminal.
I have a 6-core AMD 64-bit processor; 8 gig of memory; a GeForce GT520 dual-monitor setup; running 64-bit Ubuntu 12.04;