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.