I have squaretrade on my iPad. I picked squaretrade because it basically covers everything except for theft. Meaning if I drop my iPad, they will fix it. If they can't fix it, they will give you a check for the purchase price of your iPad.
The only warranty claim that I have had to make was through one that I bought with best buy and it was really easy. What happened is I bought a nintendo wii with the best buy warranty...about 14 months later it just stopped working for no apparant reason. I contacted best buy and they sent me a label to mail it in. I mailed it in, and then they sent me a best buy gift card for the total purchase price (including taxes) of the wii. I am not sure if best buy will cover accidental damages.
I think that with apple care, if you accidently damage your iPad, it will void the warranty. Not sure if best buy works the same way.
I highly recommend squaretrade...even though I have never had to file anything with them most of what I have heard about them has been good.