Hey everyone:
I have an EVGA 03G-P4-2784-KR GTX 780 and I'm experiencing problems.
 
Here are the machine specifics:
MoBo:  Asus Maximus Vi Hero … I have a BIOS setting for 4.6GHz overclock but for these tests I’m running a stock i7 @ 4770K @ 3.9GHz. 
Video Card Specifics:  CPU HWMonitor indicate a VIN0 of 0.887V and a minimum temperature of 28C and a maximum of 29C
 
16GB of memory:  G.SKILL Ripjaws X Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 2133 (PC3 17000) Desktop Memory Model F3-2133C9D-8GXL.  NB Frequency @ 3900MHz Timings are as follows:
DRAM Freq:  1200 MHz
CAS# Latency (CL): 9.0 clocks
CAS# Delay(tRCD): 11 clocks
RAS Precharge (tRP):  11 clocks
Cycle Time (tRAS:  31 clocks
Row Refresh Cycle Time (tRFC):  193 clocks
Command Rate (CR):  2T
 
Monitors:  Two Asus ProArt 1920x1200s … each taking up one DVI port on the back of the card.  I have swapped the monitors to see if the problem travels along with the monitor ... it doesn't.
 
Power Supply:  Seasonic SS-760XP2 ATX 760W, 80 PLUS PLATINUM PS
 
Problem:  When viewing a simple video my second monitor shimmers and goes black … recovers … and does it again … sometimes a couple of times a minute … sometimes only a couple times a day.  Not only that but the artifacts on the second monitor are terrible as well.  I have RMAd this card once … same problem.  I also remember, when I purchased a computer from CyberPowerPC, with this same card, I encountered the same thing.  A search of the internet also shows I’m not the only one afflicted. 
 
What is going on?  At the time this was a $700 card (Ti had not yet come out).
 
I have installed the latest 337.50 (previous version was 334.89 … but I’ve installed each one as they came out in hopes a fix was found … nope).  And, as always … chose Advanced and checked “Perform  a clean installation”.  I unchecked all of the junk I neither need nor want (3D Vision Controller Driver, 3D Vision Driver, HD Audio Driver and NVIDIA GeForce Experience … leaving only the video driver).  And, Ta Da … same old crap.
 
Any ideas would be greatly appreciated.

In the interest of compliance I dropped the RAM to the stated 1066 ... even though:
 
1.  The RAM came with a DDR3-2401 9-11-11-31 2N 1.65V to 1.20V Extreme Memory Profile ... which worked wonderfully with the ASUS Hero
2.  I tested each stick of RAM, alone, for five hours or more ... using MemTest5.0 ... with no errors on any of the sticks.
 
In the time I spent testing my own machine another post surfaced complaining of the same problem.  Why is such an expensive video card plagued with such foolishness as this!