As a character, Batman has never remained static. Even the seemingly immutable elements of his mythos, namely his code against killing, are a production of constant revision throughout the years. In his earliest appearances, Batman wasn't afraid to brandish a pistol and step on a few necks to prove a point. Over the years, The Dark Knight has gone from a dark avenger and detective to a campy father figure and eventually an ultra-violent vigilante that feels more akin to Dirty Harry than a superhero. With each iteration of Batman in comics, there's usually been at least one live-action adaptation that coincides with The Dark Knight's new era-specific tone.
In the video linked above, the YouTuber Absolute Music performs an interesting medley of Batman's various live-action theme songs across his cinematic career. The video shows how pivotal a role theme plays in constructing the aura around a character as iconic as Batman.