Sven Eric Maier at 2013-06-06 14:05:53:
DIE HARD did for action movies what 12 ANGRY MEN had already done for drama.
The three Aristotelian unions of action, time and space create a very dramatic story. It's set in a contained environment over the course of a few hours with one main character set against a group of opponents. The concept was so simple, that it spawned an entirely new subgenre -- the Die Hard Scenario.
For me, the chief idea is, to hurl a cop from a different city into this kind of situation. It's believeable that someone with his training could actually pull those stunts off. It's not his jurisdiction, but since the terrorists are holding his wife hostage, McLane has a very good excuse (in the mind of the audience) to use everything at his disposal against the bad guys.