Fair use is governed by Title 17, U.S. Code, Section 110
In plain English, the straight dope is that any viewing of a film outside of a private home must be done with the permission of the copyright holder, even if no admission is charged.
There are a few library and university sites that explain copyright and fair use issues well. I especially found helpful a site at the Univ. of Texas
Major studios have agencies that provide these kinds of permissions - more info from these agencies can be found here:
http://www.mplc.com/faq.php
http://www.movlic.com/faqlibrary.html
Independent films might be easier to get permission for (or not) depending on the group, the cause, the people involved, etc. But legally you do have to get permission.
Of course the usual disclaimers apply here: we're librarians, not lawyers, what we tell you should not be construed as legal advice, etc.