Chatterbots include the Original Eliza psychotherapist
and several variations including  Dr. Webowitz, WWW Quack Psychiatwist,  Dirty Eliza, the X Rated Psychotherapist, or for a more spiritual, soothing approach, Ask Jesus at http://www.crucify.com/.    Or, for the mathematically inclined, direct some questions to Julie of Phoenix Quest fame.  Of, if you miss  John Lennon  try chatting with his online impersonator.  Perhaps the best of the chatterbot genre is ALICE the Chat Robot - highly recommended.

For additional choices, Yahoo maintain an up-to-date list.  Other AI sites worth visiting include:

A site which automatically creates a "post-modernist" essay, replete with bloated jargon and incomprehensible sentence structure, every time someone logs onto it.  This was described in the NY Times on Feb 27, story also available on this site in case the Times drops it.

Some prize-winning AI programs can be found at:
http://ciips.ee.uwa.edu.au/~hutch/hal/
in Perth, Western Australia.

Many interesting games and simulations are available at Serendip in Bryn Mawr.  A theoretically interesting one is the "Game of Life."

Ben says the following link leads to dozens of cool applets for neural nets, artificial life,
genetic algorithms, etc. This is a more advanced site, with code which can be used by those writing their own AI programs: http://www.aist.go.jp/NIBH/~b0616/Lab/Links.html

A large number of Artificial Intelligence sites can be found on Yahoo's page of Web-Based AI Sites.
Yahoo also offers a good selection of sites with information and conversation about AI.