There's no end of laugh-out-loud lines in Casablanca, mostly courtesy of Rick and Louis, but we'd be hard-pressed to refer to it as a comedy. When a movie has Nazis, betrayal, unrequited love, and murder, you pretty much have to call it a drama.
Many people think of this film first and foremost as a romance; as one of the most enduring love stories of all time, it's hard to argue that point. But Rick and Ilsa are not getting all kissy-face in a bubble. (Which would be tough to film, by the way.) Make no mistake about it, Casablanca is just as equally a movie about politics and war. There may not be as much actual gunfire as in a war flick like Saving Private Ryan, and Bergman might be the only bombshell for miles around. But the terrors of war hover over every aspect of these characters' lives, and affect every one of their decisions.