I have made a claim for my son's tablet with Square Trade, pretty simple process. The only negative was the time it took to go through the whole process. I think from the time we sent the tablet in to having a replacement sent to us was about 10 days. I have made two different claims with Asurion, one was with my Rezound, after about 21 months the buttons stopped working. Went into Verizon on Friday and had my replacement on Saturday. My daughter shattered her S3 screen. File Claim on line Saturday morning, had the replacement Monday afternoon.
I have found both to provide very good service. I keep my phones insured through Asurion, for their speed of getting the replacement and because they cover theft. With teenagers taking their phones to school I like having the theft protection. For my other electronics I have Square Trade coverage. You can always find 30% off codes. One warning and I don't know if this is an issue, but years ago when I bought my daughters iTouches on Amazon I bought the Square Trade Warranty through Amazon, I was not careful and did not realize that the option I selected was only a warranty extension, did not cover accidents. I have since made sure always buy my warranties and the Square Trade site. Plus with the coupons I get from them the price is always very reasonable.
Just be aware Square Trade may fix your device, send you a replacement device (refurbished) or they may pay you for the device. The option is theirs as to the action they will take to resolve the claim.