Well, before we go into what makes for a good action movie, we have to understand what makes a good movie. This is simple, seeing as how all movies need these things to make them good and enjoyable. You need an engaging/interesting story, well written/fleshed out characters who are relatable, and it has to be shot competently, but these are just the basics of movie making of course.
Now, with each different genre the filmmakers have to add in other elements to have them be considered an action movie, or a horror movie, and so on. So what makes for a good action movie?
Momentum and the Use of Breaks
Don't you hate it in an action movie when everything slows down and nothing of interest is happening? Once it loses its momentum, there's no way it can recover. The best examples of films that never lose that momentum are a French action film called Point Blank and Liam Neeson's infamous Taken. They each have a short set up, and once they get moving, they never stop, with each ramping up to a satisfying conclusion. When they do use their breaks, they don't overstay their welcome and they're not dragged out for 20 minutes until the next overly long action set piece starts.
The perfect example of a good use of break is in the first Taken film, when Liam Neeson rescues a girl from a construction site. He sets up the IV, and once he's done he sits down and rests. There's no dialogue, he just takes a breath and rests for a second, which allows us to see the damage that's been inflicted on our hero, and gives us some character development without being told what's going on. Because it's a short scene, it also doesn't disrupt the momentum of the story.
Real People Doing Stunt Work
The James Bond franchise prides itself on having real people doing real stunts, like Goldeneye's breathtaking dam dive scene. It would have been weird if it was all CGI, especially back then. When I see noticeable CGI in an action movie it takes me right out of it, but when you see a man actually getting hit for real, like in both Raid films, you, as a member of the audience, feel something physical.
Have you ever watched a fail video on YouTube and seen someone fall off a building? What's your reaction like? It's probably, "OHHHHH." You may cringe or laugh depending on what happens, but you do that because it's really happening. That's the point of an action film, to make it look like these people are actually fighting hand-to-hand, or shooting at each other, or running away from an explosion.
This is even more effective when you see the actors do their own stunts, like Keanu Reeves fighting baddies in John Wick, and seeing Tom Cruise actually hanging on from that plane in Mission Impossible 5. This way the editor doesn't have to awkwardly cut away from the action to see a noticeable stunt man because the actors are actually doing it themselves, which generates a real feeling inside the viewer.
Running Times and Action Fatigue
There's a great action scene at the end of Kung Fu Killer, or Kung Fu Jungle if you live in China, and it incorporates traffic. Two guys are fighting in the middle of a highway, and they have to dodge oncoming trucks and cars. It's extremely tense, and it only lasts for a few minutes. It's short, sweet, and to the point.
A lot of people criticize the end fight in Star Wars: Revenge of the Sith, and how long and drawn out it is. There is no need for a fight to go on longer than ten minutes because it is not length of time that makes a fight epic, it is what happens during the fight that does.
When an action scene goes on for too long you can get what's called "Action Fatigue." There comes a point where you just aren't wowed by explosions or car chases anymore. I had this problem in all the Transformer movies, each being well over two hours long, and filled with endless, substance-less action until it becomes just explosions for the sake of it. We get it, there is a fight going on! In Transformers 3 the climax lasts for about 20 minutes, whereas the climax in the first Die Hard lasts five minutes, which is more memorable and much more badass.
Fun Fact: Alan Rickman performed that iconic falling stunt for real. Not the part where you see the guy falling from the building (though that was real, too), but when they let go of the watch. The actor was dropped several feet and the reaction he gave was totally real. REAL!
Add All These Ingredients and What Do You Get?
Well, you get something that doesn't waste your time, is badass, and is memorable. The whole point of the action genre is to keep you thrilled and on the edge of your seat, not to bore you to death. So go check out movies like Kung Fu Killer or Point Blank, and, if you haven't watched it yet, Die Hard! Come on, there's something wrong with you if you haven't seen Die Hard!