Well, you need it anytime probability theory isn't applicable, such as when you have a set of observations that you're trying to explain. There is actually a third form of reasoning that is more appropriate than induction for such cases, called "abduction" or "reasoning to the best explanation." It's how a scientist formulates an hypothesis, for example. Stated as a logical deduction, abductive and inductive arguments are always fallacious, e.g. abduction would commit the fallacy of "affirming the consequent" if you tried to assert that the reasoning "proved" anything. But in science, it's much more useful than saying, "I can't logically conclude the explanation," because it gives you an hypothesis for further testing, more data collections, etc. to refine your "guess." Perhaps you still don't see the value of such "illogical" reasoning, but science would make little progress without it.