Many critics and a large section of the general public see Bruce Willis as one of modern film's archetypal Action Men. Strangely, only about one fourth of his production clearly falls under the heading of "action".
He made an important contribution to the action genre in the film that made him a star, "Die Hard", a movie that created its own branch of the genre and suffered an amazing number of bad rip-offs. Their lacking qualities may have "dyed off" on the reputation of the original protagonist...
If you only know Bruce Willis the action hero, make sure to explore his other movies, in the "Drama" and "Comedy" categories. There may be a few surprises in store for you.