MMORPGs (Massively multiplayer online role-playing games) are typically thought of as games that are for adults. For example, I play one called World of Warcraft. However, there are definitely adult themes there that I wouldn't want a child exposed to. Aside from violence, there are plenty of people in the public chat channels that say inappropriate things.
However, a friend of mine pointed out one that is geared towards children. This is a MMORPG created by Disney, and it is called Toontown. Like most MMORPGs, this does include a monthly fee...but it's interesting to see Disney targeting a younger audience with this.