Did you know that if you leave your kid alone on a computer it will probably wonder off to some site with content you definitely do not want it to see. It's amazing how much violence and nudity and much worse is served to us all.
But we can handle it. Kids do not know what is good and what is not. That is why we have to make sure we know what are they doing and what sites are they playing on.
If you're looking for a safe site you can let your kids to play on without worrying about content of the games I might have a suggestion. There are many good sites with nothing but games for kids and suitable content.
In search for a violence / nudity / pornography free site with games targeting young children, with games that will give them something back only just fun, I've found a good site called SuperFlashGames . In the early stages you could find lots of different games on this site but laately they publish only games suited for kids with no violence.
Different dress-up games, coloring games, puzzles, logical games can be found here. You can basically leave your kid to play and do your chores without worrying and during this time your child will be forced to think and develop it's memory, logic, sense for matching colors, etc.
There are really some great sites for kids and this is just an example. Do not forbid your children to play online just be careful what they are playing.