Growing up kids is enjoyable, you do not really want to spy on them, and still give them enough freedom to breathe, but you still would want to monitor them in a way just to ensure they are going up in the right direction.
In the information age, the Internet has been a tool that has been used in both good ways and bad ways. And I guess one concern of many parents is what do their children do online? Chatting and emails have been tools also of the malicious people looking for targets of prey, from pedophiles to scammers, phishing attempts and plain robbers getting information about your home. With the high volume of pornography, illegal gambling, illegal selling of drugs online and adult dating websites, you would want to take some extra precautionary measures.
One way to be sure is by the user of keylogger programs. A good keystroke logger can make parents feel more secure without staying over the shoulder of your children. A leader in the keystroke logging software is Spectorsoft. and you might want to check them out. They have been mentioned in several TV programs and magazines. They can monitor emails, blogs, surfing activity, chatting and more. This may also have other applications in the business world as well as in private investigation purposes.
If the kids are on your LAN there is nothing stopping you from keeping watch over every piece of traffic, unless they’ve gotten smart to SSH, HTTPS, and encrypted chat. You can have ethereal or etherpeek running on central server which can filter certain words or phrases and alert you (if you want to monitor passively). Otherwise, keylogging is the option but be prepared to pipe all that output (and the traffic your kids receive) to a text filter. You may want to force all your LAN clients to run through a proxy port which does the monitoring on-the-fly, which will allow you to funnel all traffic.