To be honest, what is your idea of 'classic literature'? It would take most novels that were written and published before 1950 right? It's a difficult one to place. For me, the classics were novels by Charles Dickens, Jane Austen and J.R.R Tolkien. I wasn't sure if childen's classics were included as I would have included The Hobbit in a heartbeat. But, in keeping with what is thought of as 'classic' my choices are below. Another thing about adapatations of classics, there are always at least 2 versions out there.
1. The Killers (1946)
This is one of my favourite noir films, in fact it was the film that peaked my interest in the genre. There have two prominant adaptations of the short story by Ernest Hemingway, published in 1927. The superior version of the this 'classic' story is of course the film starring Burt Lancaster as Anderson, a one time professional boxer who ends up working for the mob, getting mixed with femme fatale Kitty (Ava Gardner) too.2. Anna Karenina (2012)
Leo Tolstoy's epic tale of forbidden tragic romance in Russia and the film that brought it to life on screen. I am of course talking about Joe Wright's beautifully made version with Keira Knightly as the tragic heroine. The idea that the majority of the film is played out in a theatre is not only an imaginative idea but it is also explores the old Shakespeare idea that 'all the world's a stage' and that all these characters are constantly acting out their parts in the story and Anna breaks free of this 'tradition' and shows her true nature and feelings. A beyond brilliant concept and the production design is simply divine. 3. The Great Gatsby
Speaking of divine production design, Baz Luhrmann's adataptation of F. Scott Fitzgerald's masterpiece had such high expectation, people treated it like Marmite (either loved or hated it). As a big fan of Fitzgerald's writing, for me, the film captured the excess, emotion and the real reason why Nick Carraway is the narrator. These characters were so full of life, they needed an 'outsider' to tell the story and it worked so well on screen. All the leads were charismatic (except the terrible casting choice for Myrtle) and that is exactly what was needed. The Great Gatsby is my favourite book, Luhrmann did it justice.