Not counting that one Apple IIe, I've been a regular Mac Owner and user since Jan 2002. I think Applecare is worth it only on portables, perhaps only on a high end portable (MBP.. before, PowerBook), and I think only worth it if you can get it cheap. People are saying ebay here - how do the prices compare to student discount? I am a student right now.
I've always had some sort of random problem with my Powerbooks or MBPs and Applecare has come in handy (display stopped working, a charge stopped going to the battery, etc). If I didn't have Applecare, in terms of Apple's prices, it would have probably cost me a lot, but perhaps I could have shopped aroudn to soften the blow. I've also noticed apple has done nice things for me here and there. Back when I had the Titanium Powerbook and towards year 3 when all the paint was chipping, they replaced my cover for me on a random send in for some other problem. I also would slip in my wear-and-teared AC Adaptor on my previous laptops and they would send me a new one. I believe Applecare at the student discount level is like $200ish and at the price of $2kish for the laptops I bought, I have found it to be worth it.
The key thing is when you get it, try to get your money's worth. One of the things that annoyed me was when they would always try to get me to go in the store whenever I called with a problem. For a while, there was no store immediately nearby, but now there is, but even then, I still would rather them send a box and save me the time. So that's my complaint about them. If I'm shelling out a couple hundred, I want the convenience of the repair.
Other than applecare, I'm pretty anti-extended warranty. If you decide not to get applecare, I don't think you should lose sleep at night. I think at the end of the day, the odds are in your favor.
Oh, I saw homeowners insurance tossed around a bit, and when I cracked the screen of my MBP late last year, I looked into that but the deductible was $500 and the screen repair was $436 w/ my student discount so that wasn't a smart option.