Two chat bots, Alice and Jabberwacky, converse with each other. "J: Yes. Would you like to hear a joke? / A: Sure, tell me about it. / J: Why don't blind people skydive? / A: Perhaps it is impossible. / J: I think you lie a lot." (thx, nick)
Update: Rex Sorgatz ran a similar experiment back in 2002.
Update: Interviews with Robots is an entire blog dedicated to chatbot conversations.