It could get pretty intense for a kid. Once scene that I felt was inappropriate was the implied beheading of a hobbit. It was not in the book and I don't think it served any real purpose since it was not integral to the plot. I saw plenty of kids at the movie, but whether or not they were scared, I don't know.
The cast was great, and I was glad they chose such an outstanding actor as Sean Bean for the role of my favorite character, Boromir.
Where was this scene beheading a hobbit? In Galadriel's mirror? or Bree? I don't remember it.