Oscar-worthy Movie: Face to Face (1976)
Best known as Swedish director Ingmar Bergman's muse, Ullmann gained critical acclaim for her prominent roles in 10 of his most-admired movies, including Face to Face. So far, that's the only film that landed her a Best Actress nomination—never mind the fact she carried the film Persona literally without saying more than a couple lines of dialogue.
Ullman brings an intensity to her films that's hard to overlook, and yet the Academy has, time and time again. Perhaps she'll gain their attention as a director instead: She's set to start filming Miss Julie, with Jessica Chastain starring as her own muse. Bergman would be proud.