In which the action is actually exciting. The actual quality of the games may vary.

To define "good movement" the bare minimum is that it needs to be more than just a simple dodge button. Lara Croft and Ratchet's side jumps or Max Payne's dives qualify as more than just a dodge because you're allowed to shoot while moving, something that simple opens up a lot more possibilities in combat. This is why I included Uncharted 4 and its DLC but not the previous games, the grappling hook you can swing on while shooting makes for a very different experience. Even the ability to shoot while jumping alone could be enough, if there's enough airtime or you have a gliding ability like in inFamous or Destroy All Humans. Many of the games in this list also generally avoid using cover systems, but it's okay if a game has them as long as it doesn't rely entirely on them.

Why not first person shooters? I find that those that have good movement are pretty well documented and have been getting more and more popular with the return of boomer shooters, even beyond that everyone knows their TF2s (Team Fortress 2) and their TF2s (Titanfall 2). The third person perspective should, in theory, allow for even more freedom of movement since you can actually see your character, but this is rarely even attempted.

I realize most mecha TPS games could fit in here, but I'm not that familiar with that subgenre, so suggestions in general are very much appreciated, I'd like to make this list as complete as possible.