Quite a bit, actually.  In 'Computing machinery and intelligence.',
Alan Turing, one of the founders of computer science, made the claim
that by the year 2000, computers would be able to pass the Turing test
at a reasonably sophisticated level, in particular, that the average
interrogator would not be able to identify the computer correctly more
than 70 per cent of the time after a five minute conversation.  AI
hasn't quite lived upto Turing's claims, but quite a bit of progress
has been made, including:

- Deployed speech dialog systems by firms like IBM, Dragon and Lernout&Hauspie

- Applications of expert systems/case-based reasoning: a computerized Lukemia
  diagnosis system did a better job checking for blood disorders than human
  experts!

- Machine translation for Environment Canada: software developed in the 1970s
  translated natural language weather forcasts between English and French.
  Purportedly stil in use.

- Deep Blue, the first computer to beat the human chess Grandmaster

- Fuzzy controllers in dishwashers, etc.

One persistent 'problem' is that as soon as an AI technique trully
succeeds, in the minds of many it ceases to be AI, becoming something
else entirely.  For example, when Deep Blue defeated Kasparov, there
were many who said Deep Blue wasn't AI, since after all it was just a
brute force parallel minimax search (!)

ref:
Alan M. Turing. Computing machinery and intelligence. Mind,
LIX(236):433-460, October 1950. (http://www.abelard.org/turpap/turpap.htm)

Sheiber, S, "Lessons from a Restricted Turing Test". Communications of
the Association for Computing Machinery, volume 37, number 6, pages
70-78, 1994