This is my eleven year old daughter's "all-time favorite movie," and has been since she first saw it at age 8. It is truly unique among alien invasion movies because it's not really about the aliens at all, or their amazing technology, or their horrid plans for the planet - its about people, and about faith, and about how God never abandons us, even when we think He has, or even when we wish He would.
Be warned, hereafter, there be spoilers.
Graham Hess is a Pastor who has rejected his faith because of the pointless death of is wife, but who still has two kids to raise, both of whom have issues of their own. His son suffers from asthma - which both nearly kills him and saves his life before the movie is over, and his daughter has some obsession or phobia which results in her leaving glasses of unconsumed water all over the house because they're "contaminated." In the end, it's her phobia which may save them all. Tying it all together is Graham's brother, a washed up minor league baseball player known for both his monumental home-runs and his colossal strike-outs, who, in my opinion, provides far more strength both to Graham and his children than any of them realize. (Oh, and by the way, you'll never look at static interference on a baby monitor the same way again.)
The movie does provide some genuinely scary moments and overall has a tense atmosphere which plays heavily on the fear of the unknown. Some of it might bother younger children (though I think the talk about the stabbed dog is overblown - and as I inferred above, it certainly didn't bother my daughter when she was 8), but for older children it's a powerful movie about love and faith - not losing it in the face of disaster, and re-finding it in the face of Grace.