Answer:
Catch-22, the novel, holds several existential theories. There is Dunbar's theory that in order to have a long existence, you must live a life filled with boredom. Dunbar also asserts that the soldiers are very old (even though some are as young as 15 years old) because every time they fly a mission, they are very close to death. ("How much older can you be at your age?") There's the opportunist old man at the brothel who believes that affiliation is meaningless. There's the beauocratic zombieism of Doc Daneeka. Milo Minderbinder's extreme desire for capitalism. Major Major's longing for mediocrity, etc.
Overall, there is the idea that existence stops when your life stops, and that your existence could cease to be very suddenly at any moment. Yossarian is determined to live as long as he can, and every time he goes up into a plane, his only motive is to come back alive. I would also say that it has a very negative existentialism in that it seems to assert that life is filled with very harsh conditions, but it's all you have, so you either make do with the ugliness or cease to be. In some ways, it has an athiest existentialism, rejecting an afterlife.