Someone told me that he has seen software systems that:
See all other answers here about how and why it's not reversible and why you wouldn't want to anyway.
For completeness though, there are rainbow tables which you can look up possible matches on. There is no guarantee that the answer in the rainbow table will be the original password chosen by your user so that would confuse them greatly.
Also, this will not work for salted hashes. Salting is recommended by many security experts.