I’ll say this as a comment on how much my kids like it. I’ve already had to referee their first big fight over who gets to use it.
My kids use the Fire for the video more than for the apps so far, though it will be interesting to see if that changes over time. I like the Kindle Fire best as a video and Android app platform. For Web browsing the 1000 x 600 screen is unsatisfying, so I surf from our Windows computer when we’re at home. If we’re out, then the Fire is a better Web browser than my wife’s Samsung Android phone and lightyears better than my Blackberry, but so far we haven’t thought to take it with us.
I think Rex Hammock is right that iPad vs. Kindle Fire isn’t really a vs. The Fire really starts making a lot of sense if you’re an Amazon Prime customer. That’s when you start getting free TV shows, movies, and the one book a month from the Kindle lending library. The iPad’s bigger screen makes it a better browsing platform, and the iPad has a bigger app library and more gadgets like the GPS and camera.