Starting at BU:
CFA's calendar -- relevant facets are: theater; opera; fringe
More is within easy reach: Boston Early Music Festival, Boston Lyric Opera, Odyssey Opera, and conservatory-level performances at Emerson College Stage, The New England Conservatory, and Boston Conservatory at Berklee Center Stage. Fabulous student musical and opera productions also happen at MIT, Harvard, Boston College, and Tufts.
The MET. From New York, live opera is broadcast in HD to area movie theaters.
Boston and beyond, and international:
Consult TheaterMania's Boston area events for a wide range of live performances in theater-like venues, find professional touring productions through community-based work. Includes links to events in other major US cities.