Yes, I think they need to do homework, as it teaches them what they need to know for life. Think about this, when they are in elementary school, they start with 1 page of homework, and as each year passes, so does the amount of homework. Then, in mid-school, they have a lot more homework than they did before (1st - 5th). This never ends though, high school gives more homework than mid-school, and college gives a lot more homework than high school. Seriously, this teaches them the skills that they need to advance through school.
I do not think schools should assign homework. They go to school to learn. Each child has a unique home life, and some just don't have the time for hours of after school assignments. If a child doesn't finish classwork in time, that should be sent home to be finished for the next day. If a child is getting poor grades, that child should study the subject they are having issues with. Study guides should be available to any student who finds them useful. Required homework is just useless. It lowers the scores of children who know the material but get bored or don't have the time to do the homework, and it raises scores of children who really need more help understanding their assignments but instead end up falling between the cracks because their scores said they understood more than they did. Then again, that is just my view of it.