There is a lot of solid advice in this thread. It all depends on your specific situation:

* Sometimes the answer is to go work for a better boss. Someone who does constant 180s is impossible to work with.

* Sometimes it helps to learn more about business (I recommend "Lean Startup"). You'll understand the rationale for the changes.

* It might help to learn how to present/guide to options, like a consultant (I recommend "Secrets of Consulting" by Gerry Weinberg). "Do nothing" is usually a very solid option, and you have to educate your boss about it.

* You're always in control of energy/timing. Sometimes you can slow-roll a bad initiative and see if it goes away. Sometimes you can work like crazy to get a good initiative completed so that "its done already and can't be rolled back".

* You may be able to piggyback necessary work onto questionable work. So that if the core feature is canceled, you've "cemented" some small unrelated improvements in the codebase