As always, an excellent, detailed, thoughtful and informative post from GGJStudios.
I have always made a point of buying Applecare for my Apple computers (though not for iPods, or other devices from the Apple family); computers cost too much, and. if anything goes wrong, repairs can be very expensive.
To date, I have had a MBP and a MBA and I have bought Applecare for both. Strangely, the Applecare paid for itself over time. The HDD went in the MBP, and was replaced under Applecare; (GGJstudios is quite correct in saying that battery death is not covered). Re the MBA, the keyboard and the external drive were replaced under warranty, while the magsafe of the MBA has been replaced under Applecare.
The key point about Applecare is that you do not need to buy it the day you get the computer - but you must get it within the first year, and before the first year anniversary of your purchase ends - not a day over - otherwise you will not be able to buy it.
Personally, I'm a fan of Applecare; I see it as a sort of peace of mind for three years, - rather than the usual warranty of one - at which time I am usually ready to upgrade.
One of the key reasons I switched to Apple was the excellent customer service; other companies sometimes attempt to seek refuge in contractual small-print, or try to weasel out of obligations, but Apple tend to honour their warranties, hence the attraction of Applecare.
Having Applecare also helps - by making it more attractive to potential buyers - when selling on a computer if there are a few months of Applecare left on it.
Cheers