You are the only person who can decide how much, if any, computer time your child may have. Many people are vehemently opposed to young people using computers because they fear it will hurt them neurologically. Others think that a small amount of time on a computer is helpful to a child in this technological age.I see the computer as a tool in the same way I use television as a tool. For the preschool child I also believe that mom or dad should be sitting with them the entire time they are "online". You can help them by being their designated reader. They will enjoy the time spent with you and having someone to talk with about what they are seeing and doing. Even though I sit and play with my child I make sure that I have 100% confidence in the site before I let her use it. If I get up to help my other child or to take something out of the oven I want to be sure she is exposed to high-quality, family friendly sites. It takes only one accidental click for a person, of ANY age, to end up looking at junk!
What follows are game sites that I have actually used with my 4 year old daughter and have searched through thoroughly before allowing her to play. I know that I can recommend these as kid-friendly and safe environments.
Funbrain.com This is one of my all time favorite game sites for kids of all ages. This link will take you to all the games for kids age 3-6.
PBS Kids You have 2 options to find games your child will enjoy. You can click on their favorite show and then look for the game button or you can click on Fun and Games from the main pbskids.org page. Our favorite games can be found at the Between the Lions, Zoboomafoo and Dragon Tales sites.
NickJr.com Here you can play games with some of your favorite characters. Dora the Explorer is our favorite. There are many other choices on the site. The site is rather slow loading but worth it in the end.