During the filming of Die Hard, Alan Rickman was told that he was going to be let go on a count of three. They dropped him on "two," and the look of panic on his face is definitely not acted; one is not surprised to learn that he was extremely angry after that shoot was over.
From the same movie, the shot in the elevator shaft where McClane drops from the vent he was aiming for, but manages to grab the next one down was an accident on the part of the stuntman that made the final cut anyway.
Executive Meddling: When the fourth movie was being made, the studio execs forced the filmmakers to aim for a PG-13 rating, thus eliminating half the fun, including McClane's favorite word.. The "unrated" DVD version of the film fixes that problem and Bruce Willis resolved an argument over the phone with the studio over the script by asking "Who's is your second choice to play John McClane?"
The Japanese dub of A Good Day for Die Hard has an interesting casting addition: Jack McClane is voiced by Sou Nozawa, who is the son of the late Nachi Nozawa, who was John McClane (and Bruce Willis)'s Japanese voice actor until his death. Oddly enough, Ben Hiura (who is the current Japanese voice actor for Willis, who replaced Nozawa) didn't voice John in that film: He's voiced by Hidetoshi Nakamura instead, on the other hand, Mie Sonozaki (who voiced Lucy McLane in Live Free) reprise that role in the A Good Day dub.
Real Life Writes the Plot: Bruce's exhaustion from his schedule (he was also shooting Moonlighting) forced de Souza to beef up the roles of the other characters, giving characters like Al Powell (Reginald VelJohnson), Ellis (Hart Bochner), Argyle (De'voreaux White), and Richard Thornburg (William Atherton) more personality and screen time.
Running the Asylum: Arguably one of the biggest fans of the Die Hard franchise is... Bruce Willis. He apparently feels very strongly about not insulting the viewers' intelligence, and while his self-appointed "gatekeeper of the franchise" role makes directors cry, among other things it resulted in the villain of the fourth film actually getting a fully fleshed-out backstory (rather than what Willis described as a scene of "MySpace and cheerleader porn jokes").
Throw It In: The line "I wanted this to be professional...he won't be joining us for the rest of his life." was an ad lib. Much of the scene where Hans tries to use a fake American accent to pass himself off as a hostage to McClane was apparently ad-libbed after the producers discovered that Alan Rickman could do a good American impersonation.
McClane yellng "Whoa!" when he flings the parkour-using henchman off his car and into a wall; it was Bruce Willis's genuine reaction to the actor taking a bigger bump for the stunt than expected.
Too Soon: A TV showing of the second film was delayed in the UK - and instead replaced with the showing of the Sylvester Stallone movie Cliffhanger — because of a recent incident at Glasgow Airport involving a flaming car crashing into the building, and with the movie being set in an airport, they probably thought showing it would be in bad taste.
In the filmed one, McClane and Simon meet again at a European cafe well after the events of the film. In this ending, Simon gets away with the heist by turning the gold into small Empire State Building statues. McClane recaps that he was fired because of Simon's getaway. McClane forces Simon to play a "McClane Says," Russian Roulette-style game using a Chinese rocket launcher with the sights removed. Simon gets a question wrong and dies from being shot by the launcher. McClane was wearing a flak jacket which would have prevented major injury. The filmed alternate was rejected by the studio for being too dark.
In the unfilmed one, McClane and Carver head back to shore after the boat explodes. Carver notes that the villains are going to get away; McClane tells him not to be so sure. The scene cuts to Simon and his crew on board a plane when they suddenly discover the briefcase bomb that Simon had used on McClane and Carver in the park, the same one Carver gave back to the Mooks posing as cops. Presumably, the bomb used on the plane would have been a different one or not used to blow up a dam in a later sequence. Simon would then ask anyone on the plane if they had a 4-gallon jug, calling back to the disarming sequence from the park.
When the TV series 24 was coming to an end and a movie was being considered, rumor has it that they were seriously considering making a Die Hard 5 that would actually be a cross-over, with Jack Bauer and John McClane teaming up to fight terrorists. The idea was eventually abandoned (assuming it was ever actually true in the first place) in favor of making a stand-alone 24 movie. But oh, What Could Have Been...
This is the big one: Nothing Lasts Forever, the novel in which this franchise started from, was a sequel to the Novel "The Detective." Which was adapted to film starring Frank Sinatra. Sinatra was 73 at the time, but a clause in the first movie's contract meant he had a right to accept the role in the sequel before it could be offered to anyone else. In other words Frank Sinatra technically was and would have been the Original John McClane.