Catch-22, a novel.
(Book)

Bombardier Yossarian is furious because thousands of people he has never met are trying to kill him. But his real problem is his own army, which keeps increasing the number of missions the men must fly to complete their service. An attempt to excuse himself from the perilous missions he's assigned means he'll be in violation of Catch-22: a man is considered insane if he willingly continues to fly dangerous combat missions, but if he makes a formal request to be removed from duty, he is proven sane and therefore ineligible to be relieved.