Catch-22 (1970)

Captain Yossarian (Arkin), a U.S. Army Air Forces B-25 bombardier, is stationed on the Mediterranean island of Pianosa during World War II. Along with other members of his squadron, Yossarian is committed to flying dangerous missions, and after watching his friends die, he seeks a means of escape.

Futilely appealing to his commanding officer, Colonel Cathcart (Balsam), who keeps increasing the number of missions required to be sent home before anyone can reach it, Yossarian finds that even a mental breakdown is no release when Doc Daneeka (Gilford) invokes the "Catch-22" that the US Army employs. As explained, an airman "would be crazy to fly more missions and sane if he didn't, but if he was sane he'd have to fly them. If he flew them he was crazy and didn't have to; but if he didn't, he was sane and had to."

Trapped by the convoluted logic, Yossarian watches as individuals in the squadron resort to other means to cope; Lt. Milo Minderbinder (Voight) concocts elaborate black market schemes while crazed Captain "Aarfy Aardvark" (Grodin) even commits murder. Lieutenant Nately (Garfunkel) falls for a prostitute, Major Danby (Benjamin) delivers goofy pep talks before each bomb run and Captain Orr (Balaban) keeps crash-landing. In the meantime, Nurse Duckett (Prentiss) resorts to bedding Yossarian once in a while.

Following an attempt on his life, Yossarian flees the hospital and sets out in a raft, paddling to Sweden, a refuge for one of his squadron mates who successfully figured out a way to escape the madness.