Apple is the only entity with knowledge of failure rates and I doubt they're going to share it with us.
I look it at as risk-reward. My iPad recently came up on one year and I had to decide on getting Applecare for it. It's not expensive ($69) but I didn't get it. About the only thing that can go wrong on an iPad is the battery and that's not covered by Applecare. Even in a worst case scenario (dropping it and breaking it) I could replace my 16gb first gen with a refurb for $299. The risk reward is $69 for $299 and that's not a good ratio.
I am going to get Applecare for my 13" 2011 MBA when the deadline approaches. There are many more things that can go wrong (compared to an iPad) and the repair costs are insane. I can get it for $180 from LA Computer Company. Replacing the MBA with a refurb (if any were available, which they rarely are) would be around $1200. The risk reward is $180 for $1200 and that's a ratio I can live with.
I will say that in general I think extended warranties are the biggest ripoff there is in electronics and appliances. I'm not thrilled to have to spend $180 for this one but I think it's the exception that proves the rule.