You can buy AppleCare any time during the first year warranty period, so you don't have to buy it at time of purchase.
You can check your remaining warranty and/or AppleCare coverage here
AppleCare will extend the 1 year warranty for an additional 2 years, for a total of 3 years coverage from the date of your Mac purchase.
It also extends telephone support from 90 days, which is included with your original warranty, to a total of 3 years.
You cannot buy AppleCare again or renew it once it expires.
Neither the Apple Warranty nor AppleCare will cover damage from accidents, spills, etc. They only cover manufacturing defects.
AppleCare+, which provides some coverage for accidental damage, is only available for the iPhone, not for Apple computers.
Neither the Apple Warranty nor AppleCare will cover batteries that have worn out. They only cover defective batteries.
As to whether AppleCare is worth it or not, that's a matter of opinion. You'll find lots of opinions on both sides, with roughly 75% saying it's worth it. You really need to decide if it's worth it to you. If you want more information, you can search the forum, where you'll find dozens, if not hundreds of threads asking "is AppleCare worth it?" The overall consensus seems to be about 75% in favor of it.
Just one point about Applecare. In addition to extending the warrantee, it also extends free Applecare phone tech support from 3 months to three years. Without Applecare, after the three month free phone support, each call costs $50.
If you a sophisticated computer user, this may not be an issue for you. For a noob like me, the Applecare has paid for itself at least ten times over because of my need to get tech support as part of my learning process and when I have problems that I can't figure out how to fix.
Another point with AppleCare... I have a Macbook (2008) and a first gen MBA. They both had a few little things wrong with them right near the end of the three years, so I took them in. Both had various other issues fixed under AppleCare like a bad hinge on the MBA and cracked case on the Macbook. They took both laptops and looked them over and on both they replaced the top cover (keyboard) and the screens.
What I am getting at is that they really do take care of you if you have issues and it is a computer, so you are likely to have issues.