It's because it's different and unconventional. That's why everybody likes it.
The huge lack of dialogue in the first half of the film allows it to focus on actions and character building without resorting to cheesy one-liners. The second half of the film has a plot captivating enough to keep children interested, and even though adults pretty much realise by now that it'll have a happy ending, we still want to know how it becomes happy (come on, we've all been there).
But the most gripping part of the film, for me at least, was that it is (at least reasonably) plausible. Disney and Pixar have done their homework - in a sense - and figured out that we're in an obesity crisis, an age where technology is slowly taking over (in fact, this film has almost taken technology to levels that I, Robot managed), and over polluting and overpopulating the Earth. Is it, therefore, a warning? ...well, yes, it is. Don't get obese otherwise robots will take over. That sounds pretty plausible to me (!)
But that aside, it's a bit of fun. Children go to see it as it is aimed at children. Adults go to see it with their children and have a chuckle. Adults who don't have children go to have a chuckle anyway. This sort of family togetherness is being achieved by more and more films (Over The Hedge and Madagascar, among others). Good on them. WALL-E has popularised such family films more.