If I had to pick one film maker that has had the largest impact on modern action cinema; I would have to say the late Sam Peckinpah.
In his day he was looked upon as a renegade by the Hollywood system, as he was not willing to be manipulated into what they wanted. Peckinpah was known for filling his films with bleak themes of moral corruption and populating with the strongest anti-heroic characters you can imagine, then topping them off with innovations of extreme violence and poetic gun play.
All you have to do is look at any revered action director from this era and you will see the influence Peckinpah has on them. Whether it be John Woo and the use of gorgeous slo-mo. Even Michael Mann and the moral ambiguity his characters face; or even Robert Rodriquez and the meticulous use of coverage to be able to piece together the most exciting action scene possible.
I urge you to pick up anyone of his films such as “Straw Dogs”, “The Wild Bunch”, “Cross of Iron” or “Bring me the head of Alfredo Garcia” and try not to blown away by a master at work.