Apocalypse Now, directed by Francis Ford Coppola, is best known as a film about the Vietnam War. However, what is less known is that it is also a Grail Romance, based as much on the poetry of T.S. Eliot and the anthropological studies of James George Frazier and Jessie L. Weston, as it is on Joseph Conrad's novel Heart of Darkness.
Now, it has been argued in the past that Heart of Darkness is itself based not only on Conrad's experiences in the Belgian Congo, but also on Chretien de Troyes' Grail romance Perceval, with Marlowe as the questing Perceval, Kurtz as the Fisher King, and the Congo as the Waste Land (or perhaps Kurtz's madness, or perhaps even the Europeans' attitudes towards imperialism; this is all up for debate). Coppola's film hammers home the point, however, by incorporating the poetry of T.S. Eliot, particularly "The Hollow Men," "The Love Song of J. Alfred Prufrock," and "The Waste Land." Moreover, as has been pointed out, on Kurtz' bookshelf are copies of The Golden Bough, From Ritual to Romance, and the Bible.
Now, as The Golden Bough is about pre-Christian fertility cults, and From Ritual to Romance is Weston's application of that work to the Grail quest, it is important to point out that Eliot's "The Waste Land" was influenced by Weston's book, applying the theme of the Waste Land to post-World War I society. Coppola is applying this theme to Vietnam-era American society.
The Grail quest originates with Celtic myth, though it admittedly as analogies in other religions. The story goes that the Fisher King has been made impotent because of his sins: he is castrated, and because of the mystical Celtic (and really early Indo-European) belief that the health of the king is tied to the health of the land, the land is no longer fertile--people are dying because of his sin, which is usually a sexual one (rape, or falling for an evil woman; in some later ideas, there is an implication of homosexuality). However, the Fisher King posesses a magic vessel of plenty--the Holy Grail--which is able to sustain his life. This is as much a curse as it is a cure, for he cannot die and be relieved of pain. After many years, the Grail knight Sir Perceval comes in search of his uncle, the Fisher King. After an initial failure to heal the king, Perceval returns, and either heals the king or lets the king die and be relieved of his pain. At this point, Perceval takes his place as the new Grail King and keeper of the fertility of the land.
Capt. Willard comes in search of mad Col. Kurtz, who has committed numerous attrocities and currently has a cult worshiping him in the jungles of Cambodia. The Vietnam War is raging, and Willard's search through the jungle is as much a search for himself and for truth as it is for Kurtz. Upon reaching Kurtz, he finds the colonal half-insane, quoting from Eliot and holding pagan rituals. Bodies litter the jungle, not from war but from Kurtz' devotees. Though Willard respects Kurtz, by the end of the film he knows there is no turning back--he must be stopped so as to restore order to the land. As the people outside slaughter a sacrifical cow, Willard slaughters Kurtz with a machete in an act of sacrifical king-killing, comparable to the release of the Fisher King or the ritual sacrifice of Osiris-Attis-Adonis-Jesus-Mabon etc. Willard is the new king, ready to restore order. Here the film ends.
There is no magic vessle as a Holy Grail, and really, unless one is obsessed with the Christianized versions, the vessel isn't the most important part of the myth; the restoration of fertility and order to the land is. With this in mind, Apocalypse Now works as a modern Grail legend.
Finally, as pointed out in other nodes, Kurtz quotes from "The Hollow Men"; "The Hollow Men" quotes from Heart of Darkness; Heart of Darkness inspired Apocalypse Now.