Not accidental damage, but for my first iMac (2009 27"), after a year or so, I noticed what appears to resemble a liquid stain down the middle of my screen. Only appeared on light colored backgrounds. I had Applecare, so I took it into the Apple Store and once they confirmed it, took it no questions asked. A week later, i went and picked it up to find they replaced the screen, and logic board. Repair would have been $1600. My price? $0.
My thought is that iMacs are not easy to fix, and cost an arm and a leg to buy, and to fix. For $169, I have piece of mind that I will not have to worry about it at all for 3 full years.
I've also called Applecare and received support when my Airport Extreme went belly up...Applecare for iMac covers all connected Apple devices too. Since the Extreme was connected to the iMac, it was covered, and I got a new Airport Extreme out of it.
I never do extended warranties...except on Apple products because I know they honor it, and honor it without question.