Edward Feser, writing in reply to atheist Keith Parsons, argues succinctly that denying the principle of causality is incoherent. This of course has great relevance for debates over the arguments for the existence of God, and for responses to major objectors like Hume.
I would also argue that PSR, rightly understood — that is, in its Scholastic version rather than in the Leibnizian rationalist versions usually considered in contemporary discussions of the subject — cannot coherently be denied. Consider that whenever we accept a claim as rationally justified, we suppose not only that we have a reason for accepting it (in the sense of a rational justification), but also that our having this reason is the reason why we accept it (in the sense of being the cause or explanation of our accepting it). We suppose that our cognitive faculties track truth and standards of rational argumentation, and that it is because they do that we believe the things we do. But if PSR is false, then we can have no justification for supposing that any of this is really the case. We may in fact believe what we do for no reason whatsoever, and yet it might also falsely seem, again for no reason whatsoever, that we believe things for reasons. And our cognitive faculties may have the deliverances they do for no reason whatsoever — rather than because they track objective truth and standards of logic — and yet it might also falsely seem, for no reason whatsoever, that they do track the latter.
In short, either everything has an explanation or we can have no justification for thinking that anything does. No purported middle ground position, on which some things have genuine explanations while others are “brute facts,” can coherently be made out. If there really could be unintelligible “brute facts,” then even the things we think are not brute facts may in fact be brute facts, and the fact that it falsely seems otherwise to us may itself be yet another brute fact. We could have no reason to believe anything. Rejecting PSR entails the most radical skepticism — including skepticism about any reasoning that could make this skepticism itself intelligible.