Aside from the obvious, which we'll cover in a future Franchise Face-Off (or, if you prefer, you can read Matt Zoller Seitz's in-depth appreciation of its 25th anniversary here), Die Hard is a masterpiece of spatial composition and the characters' relation to the camera frame. The production design by Jackson DeGovia, for example, or McTiernan's staging of certain shots, which constantly arranges actors and objects in trianglular formations:
The Nakatomi corporate logo is also trianglular in shape*:
*DeGovia's design originally resembled a swastika, but McTiernan balked, so it was changed to look like a samurai helmet instead.
Would it surprise you to learn that John McClane (Bruce Willis) is not the protagonist of this particular story? Screenwriter Steven E. De Souza says in the DVD text commentary that "[t]he hero isn't always the protagonist. The villain isn't always the antagonist. The protagonist is the person who starts the ball rolling[,] so the protagonist of Die Hard is Hans Gruber when he decides to rob this building.... Once you realize that the hero in these movies is usually making the second chess move[,] you realize your obligation to give serious credence to the plans of the criminal." As if to emphasize this, McTiernan and his cinematographer, Jan De Bont, do their best to diminish McClane in stature, often framing him in doorways and sandwiched in between objects...
... or pushing him to the far left of the screen, so that the other two-thirds dominate the frame:
Even the camera does its part to exert control over McClane. Again, from the DVD text commentary:
This is obviously different from the way Hans Gruber (Alan Rickman) is portrayed in the movie, which places him front and center (and in control) of almost every frame:
Finally, a note on the film's claustrophobic feel. McTiernan not only tries to box his hero in at every turn, he restricts the viewer's sense of space as well. He does this by making the exteriors feel just as cramped as the exteriors - using a shallow depth of field, say, so that only one or two actors are in focus in the foreground while everything else is blurred to the point of abstraction in the background:
Minor details, to be sure, but proof that its makers had more on their mind than simply blowing stuff up real good. Above all, Die Hard endures today because of its storytelling, both visually and structurally. Not even its sequels could claim that.