I think you guys are over calculating the amount it takes to power a single 780. I have a 650 watt gold seasonic psu w/ a 780 and I rarely crash. If I do it is because I'm running all sort of crazy stuff on my other monitor that i know sometimes causes conflicts and locks up my pc.
In short:
1. Check ALL drivers for your hardware
2. Check back ground programs (don't be running origin and shiz like that)
3. If you overclocked your card that maybe it.
4. If you run sweetfx that may be causing it as well. (even more so if you are part of "fight club") and run the thing that should not be named.
Oh based on your current info, gigabyte card... maybe you have a lemon. May have to rma :/