Die Hard was in the 80's but it feels like more of a 90's movie to me. It was really ahead of its time because he was every bit as badass as Schwarzeneggar and Stallone, without the juiced up muscles. It was the beginning of the end of our acceptance of terrible acting because the action was good. We were like, "Wait, we can have good acting and awesome action?" Seagal and Van Damme's days were numbered. Schwarzeneggar and Stallone kept doing their thing a while but Hollywood didn't find them comparable replacements. Those action roles started going to guys like Liam Neeson and Keanu Reeves.
Die Hard was also kind of a nod back to the Dirty Harry/Death Wish era of good guy with gun, except the scale of the movie was so big and the practical special fx were awesome.