Kanopy: Kanopy has some theatre including the BBC Shakespeare series, several plays from the Wooster Group, and others.
Films on Demand: Films on Demand is mostly documentaries but has some plays as well.
Digital Theatre: The Best of British Theatre: Rent or buy full versions of plays and operas from the British stage. Interviews and trailers are free to watch.
EnScènes: Le Spectacle Vivant en Video: Nearly 1,000 freely available performance video clips and 60 interviews featuring all areas of French performance (theatre, street performance, puppetry, circus, dance, and opera) from the 1940s to the present. The videos are embedded in historical/contextual essays.