I have always had Applecare on computers, and on my iPad. To be honest, I never bothered with it for iPods (although when things went wrong, repairs/replacements were indeed covered under the initial one year warranty).
Re Applecare, I have had occasion to use it on my original MBP; the Hard drive failed after about two and a half years, and was replaced without any problem. Likewise, my first MBA had a Magsafe and a keyboard replaced under Applecare. So, yes, for computers, and other high value (and high costing) devices, I am a big fan of Applecare.
It gives me peace of mind for three years. This means that my buying cycle is not annual, but is tied into the Applecare cycle instead. Thus, I begin looking for a new computer around two and a half years after I have bought a computer (not when a new upgrade, or model) comes out.
It also means that it is a bit easier to sell; people like the idea of being able to buy a computer with a bit of Applecare still on it, and, while it doesn't add enormously to the value, it does make selling a bit easier, should one choose to go that route.