Yes! There are many, many child-friendly websites! In terms of things that you can sign up for, ClubPenguin.com is a popular website-you can choose between Standard Chat, where you can type in things to say (unless in a Ultimate Safe Chat server) and Ultimate Safe Chat. For kids under the age of 13, it's best to pick USC.
Chat with our AI personalities
One I know of is Virtual Family Kingdom. Go to virtualfamilykingdom.com and click on a link in the sidebar, I believe, that says "VFK Constitution" or something similar. Read that and it tells you what VFK does and doesn't allow. For instance: bad language, no bad words (stupid, dork), etc.