Applecare really is a hot topic, but let me just say this:
By the numbers (probability and such), Applecare is NOT a good idea.
However, you will read plenty of emotional responses which tell you how Applecare saved people when they needed it most and such, so make what you will of it.
AppleCare is a lot like any other form of insurance; a losing proposition to the insured if they never use it, but greatly softens the blow of damages and often more than pays for itself in the rare cases when damages actually do occur. And like insurance, Apple wouldn't offer AppleCare if it didn't make them money.
Think of it this way: if you plan on keeping your computer a long time (3 years) and you don't think you can afford to pay several hundred in repairs if it breaks down (or buy a new system if it's too expensive to fix), then get the AppleCare before the warranty expires.
Also bear in mind that Apple is, unfortunately, quite stingy on telephone tech support, and without AppleCare will charge you to speak to them on the phone after 90 days. If you don't have an Apple Store near you that you can go to for help, then consider this too when thinking about AppleCare.
One last thing: Applecare is
different from most insurance in that it won't cover physical damage due to abuse (liquid damage, physical abuse, etc.) or theft. It just covers breakdowns due to defects or reasonable wear and tear. For that, you should check with your credit card to see if they offer coverage, or with your (or your parents) homeowners policy to see if they cover it.