The first installment of Michael Cacoyannis' "Greek tragedy" trilogy (the other two parts, 1971's Trojan Women and 1977's Iphigenia, are also well worth seeing) is a spare, striking, and powerful film and stars the great Irene Papas in the title role.
When it comes to ranking Jean Cocteau's best films, his take on the Orpheus myth with Orphee is arguably second only to his version of Beauty and the Beast. A visually inventive and beautiful film, this is a must-see for any true cinephile.
You can see more "realistic" looking effects in any number of films today, but none of those effects will have the same kind of charm as those created by Ray Harryhausen in this classic adventure movie.
Winner of the Palme d'Or and the Academy Award for Best Foreign Language Film, Marcel Camus' Brazilian-set reimagining of the Orpheus myth is vibrant, alive, and essential.
Jules Dassin's A Dream of Passion is a difficult film to track down, but totally worth the effort. The story of an actress (Melina Mercouri) starring in a stage production of Medea who tries to connect with her character by connecting with a "real life" Medea (Ellen Burstyn), the film is not just about the Medea myth, but about how contemporary culture relates to the culture of antiquity, and it's a visceral viewing experience.