I would like to see the results of your survey on logic board failures, poikkeus, out of sheer curiosity.
My mid-2010 MBP 15" is having the same issue. Has been for years, although until just recently I was unaware that Apple was replacing logic boards for free. I brought the computer to my local Genius bar when it first started showing signs of failure. The screen was pixelating and getting all jumbled and displaying strange patches of color. When I brought it in the Genius reset the NVRAM, and sent me on my way.
This seemed to work for a couple of days, but it is difficult to say whether or not resetting the NVRAM had anything to do with the performance because at the time the problem was occurring relatively infrequently. After a couple of days the issue was back, only this time the screen turned to black rather than displaying a pixelated mess. The computer continued to run; if a video or music were playing before the screen went to black, the audio continued to play and I was able to use the spacebar to pause and continue playback. The only solution to the problem was to do a hard reset. Not ideal, by a stretch.
I tried resetting the NVRAM again. I read that sometimes this reset doesn't always "take" the first time around, so I followed the suggestion to do a few NVRAM resets in succession. To be clear for anyone looking for suggestions, I'm not sure if there is any science behind this procedure. Besides, if this did help, it did so immeasurably. That is, the problem persisted. In fact, it got arguably worse: rather than the screen going black, the computer began to reboot itself automagically, often three or four times in a row. I suspect the reason the computer's behavior changed in regards to how it handles this issue is due to software updates. When the issue began I was using 10.6, I am now on 10.8.
At this point (Summer 2012) I had resigned to the fact that there was no solution to the problem save purchasing a new computer. I have simply lived with the issue - which tends to present itself at levels of varying frequency - this past year.
So here we are in October 2013, and the problem has become so persistent I was again motivated to set to digging around the 'net for some solution - any solution - that may at the very least alleviate these impossibly frustrating crashes. I found a workaround with gfxCardStatus, with which you are able to control graphics switching. Apparently the problem occurs when switching from integrated to discrete graphics. What I've done is turn off automatic graphics switching entirely, which means the NVIDIA card will used 100 percent of the time. A bear on the battery, yes, but if it makes this thing keep running even just 10 minutes longer in between crashes I will be satisfied. This solution has helped tremendously, although I do still experience the occasional random shutdown.
One more thing: I am running Windows 7 Ultimate x64 on a Boot Camp partition of my boot drive. I have installed the latest NVIDIA driver for the GT 330M, downloaded from the NVIDIA website, as opposed to the video card driver supplied by the Boot Camp driver kit. I have not had a single crash resulting in an involuntary reboot. That's not to say there are no problems, however. Highlighting the fact that this is certainly a hardware issue, from time to time the screen goes black. In Windows though, the display pops back up after a few seconds, along with a tooltip saying the "NVIDIA driver has crashed, but has been recovered." This can be an annoying problem, especially when it happens several times in a row, but that's all it is: annoying. The display crashes, reboots, and you go on with your day. No programs crash along with the display and, most importantly, the OS never crashes as a result. No data is lost.
Right now I am typing this from within Windows, where I have been for the past couple of weeks since making this discovery. What's more, I don't feel compelled to copy and paste this text into an editor for saving in case the computer crashes as it inevitably would in OS X.
Message to Apple: Take a page from Windows playbook. If you aren't going to do anything to fix the real problem (hardware), then at least make it a little more tolerable for your users. If you've decided there is nothing to be done - no saving us - then have the humanity to treat us like a terminally-ill patient, and make comfortable as we exit this world for good. Because with the existence of this problem and the way you have handled it, there are more than a few of us you may never be seeing again.
p.s. Apple: Please tear only this one page out of Windows' book. Directly burn the rest.