Three weeks ago my GTX 570 SC HD had to be RMAed (again); so while waiting, I put in my previous card, a GTX 275 CO OP.  It is an RMAed card as well, having been RMAed in August of 2010.
 
Tonight, after being away for the weekend, I'm playing Star Trek Online when green "waves of dots" appear on the screen, which goes garbled, and the PC crashed.  Hit the reset button, and the POST screens looked normal, so I figured it was just a software crash.... well.. before Windows 7 finished loading, parts of the screen flickered green dots, causing another reset, and now the POST screens were scrambled - this is exactly the same failure mode I saw when my first GTX 275 CO-OP died.  Waiting a few minutes and turning it back on did not help.  Lucky for me, I still had this PCs first video card- a GTS 250.  I put that in, and the PC works again, which should get me by until my RMAed GTX 570 SC HD arrives tomorrow.
 
For the record, my power supply is a Corsair TX650.  The two GTX 570s that have died on me have had different failure modes - the first GTX 570 SC HD died in a similar manner to the two GTX 275 CO-OPs, while the most recent 570 would run Windows fine, but do a solid screen crash if any "stress" was put on the card (like Skyrim or TF2, STO, etc, though Civ 4 didn't crash it).  Since the GTX 275 CO-OP actually had HIGHER power requirements than a GTX 570; I reasoned my power supply is still good.
 
I know there's such things as bad luck, but for four videocards to die in four years on the same system makes me wonder if A. RMAing this 275-CO OP is a good idea since it'd just be a "Backup" video card; B. If my 2nd-RMAed 570 SC (third one of those) is going to die on me too.  The motherboard is an EVGA x58 SLI.
 
I guess my main question is: Is it possible for a power supply to kill videocards (however slowly) while not damaging the rest of the system? Or is this just Really Bad Luck?  I can't afford to buy a new system, or even a new video card right now.
 
Thanks in advance!

Honestly, to me, it sounds like the PSU is the culprit. Depending on how long you have had the PSU, they can actually quit providing the same level of power as they once used to. Using PSU's actually deteriorates them and as such, their efficiency and even their ability to provide solid power can falter as well. While you're still within reasonable wattage for that PSU, truth be told is that it's probably on it's way out and is taking your cards with it.

They aren't from four different generations - two were GTX 275 CO-OPs and two were GTX 570 HD SC's.
 
I'd hate for it to be the power supply; when the most recent card failed, I tried to unplug the P/S, but the four wire power connector behind the CPU wouldn't come out; and I was disinterested in the possibility of damaging my motherboard.
 
And no, nothing else has died a strange death, and there haven't been any power issues in this room.  I'd replace the PSU tomorrow if I had the money... and knew a good way to get the four wire power connector out safely. (There is like zero clearance on the X58 SLI, especially when installed in a case.)