Not online, but you might try checking to see if your local library lends out computer games. We've found some really nice ones that way. My kids don't play computer games very often, but occasionally we'll let them play the Maisy game, or Freddie the Fish or something like that.
I think this one might have been mentioned, but Alivia really likes the Elmo Potty game here: http://www.sesameworkshop.org/. You just have to randomly click a button every few minutes. It gets REALLY annoying REALLY fast, IMO, but she likes it. We haven't played it in a while, and I've been avoiding reminding her about it! :