Silent film, released in 1927. It was directed by Victor Fleming and written by Lajos Biró and Jules Furthman. No copies exist today, making it the only acting-Oscar-winning film to be completely lost. German actor Emil Jannings won a Best Actor award for this movie (and later for "The Last Command", which is still around).

Jannings plays a bank clerk who is assigned to deliver a parcel to Chicago. He is robbed while traveling by train from Milwaukee but is able to kill one of the robbers. Fearing that his actions will devastate his family, he switches identities with the dead robber, cutting himself off forever from his loved ones. Eventually, he becomes a beggar and is only able to catch brief glimpses of his family through the window of their home. (Remade today, the ending would feature a tearful reconciliation, explosions, boobies, and Pikachu)

Jannings' career in Hollywood ended with the end of the silent era. He returned to Germany and starred in some films produced by the Nazis. "The Way of All Flesh" was remade in 1940, but all that remains of the original is five minutes of footage.

Sources: http://www.filmthreat.com/Features.asp?File=FeaturesOne.inc&Id=441 and the Internet Movie Database (www.imdb.com)