In most instances, permission should be sought before displaying movies publicly on campus, regardless of whether admission is charged or not.
Copyright owners, among other things, have the exclusive right to authorize others to display their work publicly. Generally speaking, what this means is that permission needs to be obtained before showing a movie in a public place (including an auditorium or meeting room). It does not matter whether admission is charged or not. If more than a handful of people are invited to attend the movie, if open invites are extended, or the viewing is advertised, it is likely that the viewing is public and requires permission. Small private showings (i.e. a handful of people who have been specifically invited, a few friends in a dorm room) do not typically require permission.
Some exceptions to this general rule do exist. Pursuant to Section 110(1) of the Copyright Law, movies can be shown without permission in a face-to-face teaching setting. Most commentators (and Universities) interpret this to mean that a faculty member needs to be showing the movie in connection with his/her class. (The movie does not, however, have to be shown during scheduled class time.)
A movie can be shown if it falls under the “fair use” exception to the copyright law. (See Using Copyrighted material above). Entire movies shown by students to large groups for mostly entertainment purposes would not fall under the fair use exception.
For more information check out the Swank Films copyright page here.