If you want a conversational AI that lets you share and discover interesting conversations with others, Cleverbot is a good choice. It's contextually aware and lets you share and rate quotes. You can also pick up where you left off and have multiple-conversation histories. The service uses cookies for targeted advertising, so be warned.
Another interesting service is ExperAI, which lets you have more in-depth conversations with AI experts on particular subjects. You can share context and discuss with others, so it's good for exploring subjects in more depth. That's particularly useful if you want to explore a particular area in more detail.