It irritates me slightly when people misuse the term 'catch-22', since the definition is somewhat more complex than a simple paradox. In fact the catch is as follows:
'Fear in the face of danger that is real and immediate is the product of a sane and rational mind'
This is only a paradox when combined with the fact that the Doc has to pronounce you mad before you can be sent home. It is therefore a 'catch' - a snag or flaw in the simple plan to escape the horror of war by saying you've gone mad. It is the simple beauty of the catch that fascinates Yossarin; it is inescapable yet subtle. Similar situations are: getting a job without a house or getting anything without experience.
20th June 2001:

I recently thought of a reasonable example of a catch-22 that follows the spirit of the origional. Consider checking out books from a library; to the librarian, this is bound to lead to damage - since the outside world is full of book-damaging situations. Therefore, the following rule is the only sensible solution:

Sensible library users are those who would not allow books to become damaged.
Combined with the rule that says borrowers can only be sensible users, this means that by asking to become a borrower you disqualify yourself. Actually, the job/house or job/experience paradoxes (which were very much on my mind a year ago:) are not like this - they are bootstrap problems.

A true catch-22 is a locked loop, where you can be in one of two states, A or B. If you are in A you are allowed to be in B - but by moving to state B, you disqualify yourself from remaining in that state.