To limit myself to one genre of movie would really not do any kind of justice to my tastes. A lot of times, the most fun and appealing to me involve some kind of supernatural phenomenon in it that would normally suspend the normal rules of physics albeit magic or otherwise. The best stories tend to me leave me feeling fulfilled and like it were worth the time invested.
If I had to recommend a film to watch, it would be The Last Samurai Starring Tom Cruise. In it Tom Cruise is a Civil War veteran spending his time doing these shows for Remington, a gun company. He is invited, and accepts, an invitation to go to Japan and train warriors for the newly industrialized country. He is captured by the Samurai and learns their ways. It is a beautifully well done movie enhanced by the compelling story and possibly the most amazing movie score done to date. Here's a clip
Citizen Kane is often considered the absolute best film of all time. It was the first appearance of Orson Wells, both the star and director of this legendary film. It transcended the time by telling a story through various people of the main characters life at the stages of his life following his rise and death. This put Wells on the spotlight and was his best work he had ever done.