This article is from the rec.arts.movies.current-films FAQ, by Evelyn C. Leeper email@example.com with numerous contributions by others.
There are many web sites for this, including:
In many areas, there is also a phone service to help you. Call
777-FILM (*) and follow the instructions (you punch in the first three
letters of the film title and your ZIP code) to find out the theater
closest to you with a particular film, and the remaining show times.
You can also order tickets by credit card through them.
(*) In some areas it's 444-FILM or 222-FILM or possibly something else.
For something more esoteric (like films that play at universities,
libraries, etc.), you're out of luck unless you know the distributor
and call them.