People who like deep, thought-provoking cinema love Apocalypse Now. So do people who love violence. Apocalypse Now caters to both the sophisticated cinephile and the lover of explosions and severed heads. In other words, it has something for everybody (except for a prominent female character). There are random fan sites like this one testifying to the intense feelings people have about the film.
Directors like the movie, too. Wes Anderson, a director dear to all hipsters, is clearly a fan. In his movie Rushmore, the main character, Max Fischer, puts on a high school play based on the Vietnam War, which features references to Apocalypse Now—particularly, soldiers carrying surfboards.
The movie makes almost every "Best Films of All Time" list, so you're obligated by law to love it. "I love the smell of napalm in the morning" was #12 on the American Film Institute's list of the 100 Greatest Movie Quotes, and Apocalypse Now was #30 on its 100 Greatest Movies list.
Deal with that #31, The Maltese Falcon.