Yes they should. Besides the danger, mentioned by Emiley, I have seen children become antisocial and withdraw. They seem to loose (or never gain) good interpersonal skills. Be it with other kids, or adults.
I firmly believe they should not be denied the internet altogether, but neither should they rule on the freedom to be on it as they want to.
A parents job is not easy, but if done correctly, can bring results in well balanced, healthy individuals. Discipline is nat a BAD word, nor is it a negative action. It simply seeks to establish good habits, not to punish.
Set internet times, routines, and guidelines, and the STICK to them. The worst ting is to disregard the rules you set up. If you need to disregard your own rules, then why set them in the first place?