Childrens shows, when advertising extra online content or games connected to an episode, are obligated to include a message that a child needs to ask their parents before they log on. This is because the internet is a very dangerous place for any young impressionable mind and allowing young people to wander it without oversight is a terrible risk.
Parental Control Software is an important option and tool to be used to combat this risk, but it cannot be the only defense you use. Talk to your children about their limits and your expectations, and why it is that they cannot log in without you there. But, when they grow older and need to use the internet without you present, make sure you are still overseeing their activities using the right software.
This software should include more than a basic filters. These filters are great for keeping inexperienced internet users from accidently stumbling upon porn or other known objectionable sites, but very bad at controlling user v. user interaction or watching for potential interpersonal abuse.
You need a program that includes basic schedules which can be set to limit the amount of time your child can be online (protecting against information overload) and key logging software to watch for objectionable language or keywords in risky behavior.
This will protect against hate speech and sexual messaging from friends or pedophiles on chat services. And, absolutely, do not neglect setting a good example in word and deed for your children. If they find that you are looking at what they cannot the damage may be extreme.