"The Drama Genre is arguably the most common and straightforward film classification."
The Drama Genre may be a tad on the pedestrian side as film genres go, but it's definitely the "bread and butter" of genres as well. Many films could certainly be considered in this film style, and their entertainment value is not diminished in any way because the genre is so common.
This film genre usually deals with serious emotional conflicts between the main character and other characters, or a social reality, or even nature itself. It's the conflict and how it resolves that creates the actual dramatic elements of the movie. Typical themes for drama would be racism, addiction, crime, poverty, corruption and religion.
Some classic examples of drama films are The Godfather (1972), Schindler's List (1993) and The Shawshank Redemption (1994). Many times films such as these have an unfair advantage at the awards table. The Academy Awards seem to shine their lights on drama films more frequently than any other genre.
Tim Robbins and Morgan Freeman in The Shawshank Redemption