When I write code I only write the functions I need as I need them.
Does this approach also apply to writing tests?
Should I write a test in advance for every use-case I can think of just to play it safe or should I only write tests for a use-case as I come upon it?
I think that when you write a method you should test both expected and potential error paths. This doesn't mean that you should expand your design to encompass every potential use -- leave that for when it's needed, but you should make sure that your tests have defined the expected behavior in the face of invalid parameters or other conditions.
YAGNI, as I understand it, means that you shouldn't develop features that are not yet needed. In that sense, you shouldn't write a test that drives you to develop code that's not needed. I suspect, though, that's not what you are asking about.
In this context I'd be more concerned with whether you should write tests that cover unexpected uses -- for example, errors due passing null or out of range parameters -- or repeating tests that only differ with respect to the data, not the functionality. In the former case, as I indicated above, I would say yes. Your tests will document the expected behavior of your method in the face of errors. This is important information to people who use your method.
In the latter case, I'm less able to give you a definitive answer. You certainly want your tests to remain DRY -- don't write a test that simply repeats another test even if it has different data. Alternatively, you may not discover potential design issues unless you exercise the edge cases of your data. A simple example is a method that computes a sum of two integers: what happens if you pass it maxint as both parameters? If you only have one test, then you may miss this behavior. Obviously, this is related to the previous point. Only you can be sure when a test is really needed or not.