There is a phenomenal depth to the number of film genres that exist. Fortunately, most of them can be condensed into ten unique genres. Filmsite.org has broken it down: action/adventure, comedy, crime and gangster, drama, epic/historical, horror, musical/dance, science fiction, war, and western. Here's an infographic, which I think will really illustrate the diversity of cinema that has been and will continue to be available.