Cleopatra (partially found silent film; 1917)
Cleopatra is a 1917 silent film starring Theda Bara.  This is one of her many silent-era films to be lost (only 4 are still known to exist). Of this two and a half hour long film, only 20 seconds have survived.
Many believe the film to be among the most elaborate and expensive of its time. The film is known for Bara's risque outfits and some claim that her privates were exposed several times throughout the movie. This caused the film to be labeled as "obscene", and many church organizations tried obtaining copies of the film to destroy them. Historians and collectors scrambled to save as many copies as they could. The last known copies of the film were destroyed in fires. One was at the Fox studio vault fire in 1937, and the other fire was at the Museum of Modern Art in New York in 1958. The film has never been seen in its entirety since.
No surviving footage other than the aforementioned twenty-second clip is known to exist. It has fallen into a category with 1922 Stroheim Director's Cut of Greed as a "holy grail" amongst movie collectors.
Phillip Dye started a failed Indiegogo project to reconstruct the film, but (as of September 2016) he has found over 400 film stills and counting. Follow Dye's quest on Facebook. He is having another go with a GoFundMe campaign. On February 8, 2017, Dye screened Lost Cleopatra as a Hollywood museum.