1. The captain was a good chess player, and the games were always interesting. Yossarian had stopped playing chess with him because the games were so interesting they were foolish.
2. The Texan turned out to be good-natured, generous and likable. In three days no one could stand him.
3. Yossarian was sorry to hear that they had a mutual friend. It seemed there was a basis to their conversation after all.
4. Nately had a bad start. He came from a good family.
5. The colonel had really been investigated. There was not an organ of his body that had not been drugged and derogated, dusted and dredged, fingered and photographed, removed, plundered and replaced.
6. She was the epitome of stately sorrow each time she smiled.
7. Outside the hospital the war was still going on. Men went mad and were rewarded with medals.
8. There were many officers' clubs that Yossarian had not helped to build, but he was proudest of the one on Pinosa.
9. But Yossarian knew he was right, because, to the best of his knowledge he had never been wrong.
10. He was a spry, suave and very precise general who knew the circumference of the equator and always wrote 'enhanced' when he meant 'increased.'
11. He had decided to live forever or die in the attempt.
12. You're inches away from death every time you go on a mission. How much older can you be at your age ?
13. I've got these rubber models in my office with all the reproductive organs of both sexes that I keep locked up in separate cabinets to avoid a scandal.
14. Racial prejudice is a terrible thing, Yossarian. It really is. It's a terrible thing to treat a decent, loyal Indian like a nigger, kike wop or spic.
15. Orr would be crazy to fly more missions and sane if he didn't , but if he was sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to.
16. How can he see he's got flies in his eyes if he's got flies in his eyes ?
17. There was no established procedure for evasive action. All you needed was fear and Yossarian had plenty of that.
18. He had lived innocuously for a little while and then had gone down in a flame over Ferrara on the seventh day, while God was resting.
19. Clevinger had a mind, and Lieutenant Scheisskopf had noticed that people with minds tended to get pretty smart at times.
20. He advocated thrift and hard work and disapproved of loose women who turned him down.
21. He had observed that people who did lie were, on the whole, more resourceful and ambitious and successful than people who did not lie.
22. What could you do with a man who looked you squarely in the eye and said he would rather die than be killed in combat...
23. It doesn't make a damned bit of difference who wins the war to someone who's dead.
24. The enemy, is anybody who's going to get you killed, no matter which side he's on... And don't you forget that, because the longer you remember it, the longer you might live.
25. Her allure stemmed from her accessibility; like Mt. Everest, she was there, and the men climbed on top of her each time they felt the urge.
26. When he contemplated the many diseases and potential accidents threatening him, he was positively astounded that he had managed to survive in good health for as long as he had.
27. Yossarian owed his good health to exercise, fresh air, teamwork and good sportsmanship; it was to get away from them all that he had first discovered the hospital..
28. How much reverence can you have for a Supreme Being who finds it necessary to include such phenomena as phlegm and tooth decay in His divine system of creation?
29. Yossarian - the very sight of the name made him shudder. There were so many esses in it. It just had to be subversive. It was like the word subversive itself. It was like seditious and insidious too, and like socialist, suspicious, fascist and Communist.
30. The colonel was certainly not going to waste his time and energy making love to beautiful women unless there was something in it for him.
31. The frog is almost five hundred million years old. Could you really say with much certainly that America, with all its strength and prosperity, with its fighting man that is second to none, and with its standard of living that is the highest in the world, will last as long as. . .the frog?
32. Anything worth dying for, is certainly worth living for.
33. It's better to live on one's feet than to die on one's knees.
34. Fellow officers invariably welcomed him with excessive cordiality when he approached and waited uncomfortably for him to go away.
35. My only fault is that I have no faults.
36. Of course they had a right (to lie to you). Don't be such an ass, Scheisskopf. People have a right to do anything that's not forbidden by law, and there's no law against lying to you.
37. General Peckem liked listening to himself talk, liked most of all listening to himself talk about himself.
38. They were the most depressing group of people Yossarian had ever been with. They were always in high spirits. They laughed at everything.
39. When you consider the opportunity and power He had to really do a job, and then look at the stupid, ugly little mess He made of it instead, His sheer incompetence is almost staggering.

Source - http://www.workinghumor.com/quotes/catch22.shtml and of course Joseph Heller's Catch 22.