I hear the term Catch-22 a lot (a whole lot), and it is almost never used in the sense that Heller used it. Well, since people do like talking about how the present situation is abusing them, there are a whole lot of words and terms describing these different situations. Let's learn how to use them.
Dilemma: A situation in which you have two options, both of them bad. You can also have a trilemma or a polylemma, although no one will know what you're talking about.
Paradox: When your assumptions lead to two contradictory conclusions. When two things that seem to be true cannot both be true at the same time. (A Catch-22 can be interpreted as a paradox. See therein lies the catch-22).
Hobson's Choice: Hobson's choice is no choice at all - or more often, the choice of 'this, or nothing at all'.
Vicious Circle (or Vicious Cycle): A feedback loop in which the solution to a problem causes equal or greater problems. Or alternatively, when the only way you can alleviate a problem will make things worse in the long run.
Irony: Most often Situational Irony. There are many definitions, but I would say that Situational Irony is based on two things happening in conjunction when you would not normally expect them to, and they interfere with each other. For more on Irony, go read Gritchka's excellent writeup here.
Catch-22: Now that you know what it isn't... A Catch-22 is an option that appears to be offered, but isn't. (More specifically, a Catch-22 is the twist in the rules that snatches the option out of your hands).
I have also heard Catch-22 used to mean a Prisoner's Dilemma and Mutually Exclusive. But such gross misuse is beyond the scope of this node.