There is a HUGE difference between the kids who regularly do their homework and those who do not...The kids who do do it are more likely to be engaged in their work in the classroom and perform better academically than those who do not.
But couldn't it be the other way around? Kids that are more engaged and more academically minded are more likely to do homework? These are just my thoughts and only from my experience. I was a kid that always did her homework, and got reasonably good grades, but the reason was because I was a goody and too afraid of getting in trouble, LOL.

I agree with TFB that homework for older kids like practice exams etc is beneficial. You can't really get through your exams without studying outside of school. I disagree with it for the little kids though. A child's 'work' is play. The OP was about an older child anyway though so I'm getting off track now.