For me, fallacies are a great tool for recognizing bad reasoning, which then provides pointers about how to expose it as such using a real argument. The fallacy itself doesn't constitute a counter argument. In a good debate, the fallacies themselves never come up but you can see how they have influenced the flow of argument. I really liked how it was put in the book Logical Self-Defense: To be valid, an argument has…
Appeal to authority/experts: The fact that experts believe something is evidence in favor of it (albeit imperfect and overridable).
Appeal to tradition: The fact that things have historically been done a certain way, in a highly immodular system with complex dependencies, without catastrophic failure is evidence in favor of it (albeit imperfect and overridable).
Appeal/reduction to absurdity: Absurd ideas are usually false, even if the presumption can be overridden.
Genetic fallacy: Actually, the reason a conclusion was reached is exactly how you should judge it. (The true fallacy is thinking that you can pick an arbitrary reason a conclusion was reached -- e.g. snake dreams and Benzene -- rather than the best reason -- the later empirical confirmation of the model's predictive power.)
And so on.
Generally, the "Fallacy fallacy" is to jump from
"Hey, this piece of evidence isn't perfect (i.e. an infinite likelihood ratio, which is impossible anyway)"
to
"So I can ignore it."