You'll probably get some variance here, but generally, the goal of writing tests (to me) is to ensure that all your code is functioning as it should, without side effects, in a predictable fashion and without defects. In my mind, then, the approach you discuss of only writing tests for use cases as they are come upon does you no real good, and may in fact cause harm.
What if the particular use case for the unit under test that you ignore causes a serious defect in the final software? Has the time spent developing tests bought you anything in this scenario beyond a false sense of security?
(For the record, this is one of the issues I have with using code coverage to "measure" test quality -- it's a measurement that, if low, may give an indication that you're not testing enough, but if high, should not be used to assume that you are rock-solid. Get the common cases tested, the edge cases tested, then consider all the ifs, ands and buts of the unit and test them, too.)
Mild Update
I should note that I'm coming from possibly a different perspective than many here. I often find that I'm writing library-style code, that is, code which will be reused in multiple projects, for multiple different clients. As a result, it is generally impossible for me to say with any certainty that certain use cases simply won't happen. The best I can do is either document that they're not expected (and hence may require updating the tests afterward), or -- and this is my preference :) -- just writing the tests. I often find option #2 is for more livable on a day-to-day basis, simply because I have much more confidence when I'm reusing component X in new application Y. And confidence, in my mind, is what automated testing is all about.