We took our 12 year old the day it came out and that's about the cut-off age, in my opinion. It's very intense. We all agreed it was an excellent movie, but DS and his 12 year old friend did use some 'coping techniques' (ok, they covered their eyes a bit in a few places!) during the show. They are boys who are used to the graphic 'war games' on computer, but the big screen makes the whole thing so much more intense.
We had a terrific discussion about it afterwards, picking out the things we thought were logistical errors and what could be 'possible' and I think that helped make it less 'real'.
I would be reluctant in the extreme to take a 7 year old, but you know your children best. They may be fine with it, but I thought some of the graphic 'blood and gore' was a bit much for younger children. If they are used to that sort of thing, it really is an excellent movie.