This article is from the Theatre FAQ, by aku@leland.Stanford.EDU (Andrew Chia-Tso Ku) with numerous contributions by others.
Check out Joseph Geigel's "On Broadway" WWW homepage. It lists all
the shows currently playing on- and off-Broadway (as well as upcoming
productions) with prices, schedules, and theatre locations. It is
updated very regularly. URL: http://artsnet.heinz.cmu.edu/OnBroadway
Also check out Playbill Online's Web site.
More traditional sources for finding out what's playing on Broadway
(and off-Broadway) are the Sunday New York Times Arts and Leisure
section, New York Magazine, and The New Yorker. All three have
capsule summaries and list a phone number for ordering tickets.
Better bookstores and newsstands may carry TheaterWeek, which also
carries detailed listings. If your site subscribes to the clari.news
hierarchy, a weekly posting entitled "Broadway Boxscore" in
clari.living.entertainment lists current Broadway and off-Broadway
attractions, and ticket availability.
The League of American Theatres and Producers has a telephone line
with recorded information: 212-563-2929