The Invisible Man
(1933)

 Dr Jack Griffin (Claude Rains) checks into a hotel in a small English town, his head wrapped in bandages and dark glasses covering his eyes. He never leaves his room, has meals left for him, and allows no one to see him.  He is accidentally seen without his glasses, and they see that behind the bandages, there is nothing visible. Griffin becomes violent. The police are called. Griffin removes all his clothing, revealing he is completely invisible. He attacks the police, then escapes.

Griffin discovered a compound that has mad him invisible. However, it has also driven him insane. He goes to the house a friend of his, Dr Kemp, and reveals his desire to take over the country, since no one can stop him when he is invisible.  Kemp calls the police. The invisible Griffin escapes again. He goes on a rampage, killing people and destroying things.  He kills Kemp in revenge. The police are at a loss as to how they can catch and keep an invisible man. Griffin seeks revenge, and kills Kemp.

Griffin is exhausted, and goes to sleep in a barn. The farmer calls the police, reporting that he hears breathing, and the hay is moving, but no one is there. The police realize it is Griffin and surround the barn. It has started snowing. When Griffin exits, he is invisible, but they can see his footprints in the snow. The police shoot Griffin. Griffin becomes visible again as he dies.

Thanks Joseph C!