My iMac is about three years old. I know this because my AppleCare is expiring on November 7th, and it extends the included one-year warranty by two years to give a total of three years of coverage. In short, I'm glad I've had it and wouldn't consider owning a Mac without it.
In the last three years, I have had a hard drive replaced (December 2008), a logic board replaced (March 2010), and am currently scheduled to have a second hard drive replacement (late October 2010).
I'm not particularly hard on my computers. They've all been plugged into UPS units (I've had good success with APC) and treated well and fairly. Perhaps I'm just unlucky. Whatever the reason, choosing AppleCare is a simple matter of numbers: given the number of Macs that Apple sells, if even a fraction of 1% have issues over the course of three years, that's going to be a significant number.
Others will tell you they've owned several Macs, without AppleCare. This is the same lot who never purchase "extended warranties," which they consider "scams." To them I say that AppleCare is an exception, especially since Macs are increasingly difficult or impossible to get into. Still others will say that Apple ought to include 3 years' worth of protection with every Mac they sell. Perhaps, but the world as it exists is often disappointing compared to the world as we wish it existed.
Read on for some suggestions for getting the most out of AppleCare.
1. Always, always, always, have a current bootable backup of your hard drive. AppleCare will replace broken parts (hard drives, logic boards, etc) but they can't give you your data back. I use SuperDuper and have it run every day. Its "Smart Update" feature only updates the files which have changed since the previous backup, making it pretty fast. Carbon Copy Cloner is another option. Honestly, I don't care which one you use, as long as it runs daily. My most important files are stored on Dropbox which gives me another layer of protection. Time Machine is good, but I wouldn't use it instead of a bootable backup; in fact, I would put SuperDuper (or CCC) plus Dropbox in place before adding Time Machine.
2. Keep your Mac OS X DVD and AppleCare DVD handy. The AppleCare DVD has some tools and tests on it that you may be asked for when you call to get AppleCare support. Be sure you know where they are, because there are few things more frustrating than working your way through a support queue only to find out that they expect you to do some diagnostic test before they'll approve a repair order.
3. Get a case number as soon as possible. Once a problem is confirmed, ask the AppleCare representative for the case number. If you get disconnected, it's much easier to call back with this number. The number also confirms that they're documenting things on their end. Be sure to document on your end too: when did you call, who did you talk to, what was said, etc. You will likely have to perform a number of tests (see #2 above) and it's good to have a record of what was already tried and what happened, e.g. "was instructed to reset the PRAM and repair permissions. Did not fix the isue."
4. A long way from an Apple Store or Authorized Service Provider? Ask for on-site service. This won't apply to everyone, but it may help some folks. Typically you'll be expected to bring your Mac to an Apple Store or authorized service provider, drop it off, and then return to pick it up when it's fixed. The nearest Apple Store to me is over two hours away, and there is no Authorized Service Provider closer. Apple does not make it well-known that they have on-site service available, no doubt because they'd be inundated with requests for on-site service instead of the usual system. However, once I made it clear how far away the Apple Store was and they verified no other options in my area, getting on-site service has been very easy.
If you didn't buy AppleCare when you purchased your Mac, you can add it later as long as your Mac is still covered by the initial one-year warranty. Prices vary depending on the kind of computer you have (i.e. it's less for an iMac than a MacBook Pro). Educational users get a significant discount on some AppleCare plans, so be sure to check that out if you qualify.