Die Hard is the best action film ever made.
Hopefully that isn't a controversial statement. Certainly most people will consider it one of the best, but for me the are no other action movies that come close to John McClane's first outing. Except maybe his third1.
There are probably a dozen reasons why Die Hard is so great. Chief among them is Alan Rickman's exceptional thief Hans Gruber; smart, witty and impeccably dressed, he's always looking at the bigger picture, at the end goal - any frustration with McClane's cowboy heroics is quickly dismissed as a distraction.
If the film was made today, I have a feeling Hans' true motives - which are openly stated in his conversation with Takagi right at the beginning of the Nakatomi incident - would be hidden even from the audience until much later2. That might be a way to build tension, but the deliberate way that Hans manipulates the expectations of the LAPD and FBI elevates him from someone with unclear motives into a proper mastermind. He's got all these plates spinning, and we know it right from the beginning.
In fact, that's my favourite thing about Die Hard - all the major characters have a very clear goal that's motivating them. The overall story might not be the cleverest, but it doesn't assume that the audience is a bunch of gawping simpletons only interested in the next explosion. We know who John McClane is, what he does for a living and what his relationship with his wife is like. We like him before the shooting starts, and even if you're not actively rooting for him to get back together with Holly, you understand what his goal is and why it keeps him going when any sane person would try and escape.
I think the setting is a big fantasy fulfillment, too - unlike, say, Casey Ryback in Under Siege, John McClane doesn't have any special forces training or expert skills. He's not even especially fit or well-built. It's easy to leave the cinema thinking, "yeah, if that happened in my office I could totally take out the terrorists".
The overall message of the film - if you'll permit me to get a bit philosophical for a moment - is about facing a difficult situation head-on, rather than running or leaving it to someone else. It's why Al shoots Karl, even though he never wanted to touch a gun again: he's put in a situation where he has to protect himself and something he loves3, and he does it in the only way permissible in Die Hard.
By shooting the closest German.
1 I actually think Die Hard With A Vengeance is my favourite of the series, but have to admit that the first film is objectively better.
2 Like, for instance, in Die Hard With A Vengeance where - spoiler alert - Simon's entire bomb plot is a distraction from the bullion heist.
3 If you don't believe Die Hard's main love story is between Al Powell and John McClane, I suggest you watch their first scene together at the end of the film again.