wow, not another one.. we're not the only ones with this problem! Unfortunately I don't have Apple care (my computer is 2 1/2 years old by now) and the same problem arose with my 3.06 GHZ 24" iMac (Mac OX 10.6.5, 4GB RAM, Nvidia 8800 GS, 512GB HD).
After doing tons of research online i've found that there are MANY people out there with this issue. Unfortunately some kid who works at the Apple store compared my iMac to a car and said that sometimes things break and need to be replaced. That is hilarious because as a hobby I work on auto mechanics so I just laughed when he told me that.. Typical line he sells to customers probably.
I love apple products but after owning 7 macs, 2 iPhones, and several other accesories and apple software including using every version of mac os from 6.x.x to 10.6.x, this endeavor has been pretty disappointing. There is a serious flaw in these graphics cards it is obvious... I use the iMac primarily for email and web, with the occasional Starcraft II game (usually run not more than 1 hour at a time). I used an external fan on the iMac from time to time when I felt it would get hot to the touch (top left corner of the case). So I tried preventing any heat damage as much as possible. Unfortunately, even after installing iStat Pro and seeing that my GPU, CPU, HD temps were all in the normal range, I still had graphical artifacts and constant freezing and lockups. It got worse and worse and to the point where booting up was not an option. Took it to the apple store and within 2 minutes the guy knew it was the graphics card (did he really need to run a test? It's blatantly obvious). His attitude towards me was rude and very cold. He was rushing me to take my iMac to the back and have me drop 600$ to fix it like money was nothing for me. I had to tell him to hold on and let me think about this because graphics cards don't brake for nothing. That's when he told me I should have thought about that before not buying applecare. I was upset at the guy but didn't show it as I did not want to create a scene and make apple's reps look bad cuz I love apple and I was frustrated at this kid rather than at apple at this point. I think apple does stand by their products and I hope that they can offer some sort of fix for this rather than having us dish out this money out of our own pockets because of a design flaw (lack of sufficient cooling internally) with their products that cost roughly 3000$.
In response to this kid's comparison of my iMac to cars needing repairs: Apple is like the BMW of computers. Top of the line. Quality parts. If you buy a BMW and don't race it and daily drive it, if after 2 years your engine fails because it overheated because the fans weren't built to cool the engine sufficiently, normally BMW would issue a recall, no? Or atleast offer to replace the part as a good will for their design flaw? I would think that Apple would do the same...