I would never get Apple Care again...I got a new MacBook about 4 years ago and within 3 months it wasn't working properly. I had purchased the $250.00 AppleCare for it, and when I took it to the store they basically belittled me and said all of these things to me insinuating that I must have done something completely wrong and it was my fault and my warranty wouldn't cover it...I eventually got them to cover it but I had to jump through a LOT of hoops, and it took over a month to get them to finally agree to fix it (and only then it was because I had an article posted on consumerist.com about my bad experience...)
So needless to say, I was not very happy with my $250 Apple Care. I still love Apple products, but I learned the hard way once and won't buy Apple Care ever again. MUCH better off going through a third party.
I bought an iPod about a year after that happened and I purchased insurance through SquareTrade, which a previous poster mentioned. The iPod eventually ended up getting completely soaked in water and obviously wouldn't turn on anymore...I filed the claim through square trade and literally all I had to do was send it to them in an envelope and within a couple of days they had sent the money to me for a replacement, no hassle and no questions asked

I also have purchased insurance through SquareTrade for other electronics like my DSLR etc.
When I got my iPhone, I declined the AppleCare and opted for the insurance through Verizon. I was originally planning on doing SquareTrade, but the Verizon insurance covers it if I lose my phone so that is why I went that route.
So, in summary...I would not recommend Apple Care. I would definitely suggest Square Trade, which automatically covers you if you break the glass on the phone or drop it in water, for example. Apple Care doesn't automatically cover something like that happening, although if you give them a really hard time about it they might....
If you are worried about losing your phone, I would go through the phone company's insurance. That is what I did. It also covers me breaking my phone. The cost is higher but for me it is worth it.