You can show a movie in class because that is protected by Fair Use.
Outside of class, say at a dinner or presentation, even if it is on campus, you need to be careful.
You can definitely NOT show an entire movie without written permission from the copyright owner or without getting the public performance rights. Generally, for a non-profit, only 3 minutes can be shown from a film. Nothing can be shown at a for-profit institution without permission/public performance rights.
YouTube videos are allowed, since you are showing something from its original online source, rather than a DVD or Netflix. However, sometimes YouTube videos contain copyrighted materials. You will not get into any legal trouble for viewing material that has been illegally uploaded, but you should be aware that YouTube routinely removes these videos so something you may have been counting on could disappear.
