I would like to organize an event at which short excerpts from movies and TV shows are shown on multiple screens for ambience. Do I need a license?

It depends on whether the excerpts you plan to show are “substantial parts” of the larger works. You should not presume that even short excerpts of a long movie are not “substantial” – this is a question of fact that needs to be assessed on a case-by-case basis and may require expert advice. Contact the Scholarly Communications and Copyright Office at copyright@library.utoronto.ca.