Determinator: In the first film, he gets beat up, shot at, blown up, thrown off a building, his feet get lacerated, and he eventually gets shot in the shoulder. This does not stop him. The third film has him getting pistol-whipped, blown up, beaten, drowned, shot at, beaten, and blown up again. This makes him angry. In the fourth film, he is shot at, blown up, shot at some more, thrown out of a car, beaten up by a hot Asian chick, dropped down an elevator shaft, frozen, beat up again, shot at by a jet fighter, shot, and then shoots himself. He doesn't give up at any point.
He even gives a trope-defining little speech in the fourth movie:
John McClane: You know what you get for being a hero? Nothin'. You get shot at. You get a little pat on the back, blah, blah, blah, attaboy. You get divorced. Your wife can't remember your last name. Your kids don't want to talk to you. You get to eat a lot of meals by yourself. Trust me, kid, nobody wants to be that guy.
Matt Farrell: Then why you doing this?
John McClane: Because there's nobody else to do it right now, that's why. Believe me, if there were somebody else to do it, I'd let them do it, but there's not. So we're doing it.
Love Cannot Overcome: John and Holly clearly care about each other, but their marriage is already strained in the first movie. While Die Hard ends with them back together, ultimately their relationship can't survive John's Chronic Hero Syndrome. They're officially separated by movie three and divorced by movie four, adding to John's Knight in Sour Armor bitterness.
MacGyvering: His ability to create makeshift gadgets to save the day would make the Trope Maker himself proud.
Made of Iron: Over the course of each Die Hard movie John McClane takes a lot of physical abuse, but he still manages to keep fighting.
Manly Tears: When he fails to save a plane full of innocents from being murdered in Die Harder.
Took a Level In Jerkass: He's considerably grumpier and ruder in the third and fourth movies, but still a good man underneath.
It would be safe to assume that failing to save hundreds of innocent people from a fiery death and watching it happen right in front of him in Die Harder is an experience traumatic enough to turn anyone a bit mean and cynical.
Perhaps more importantly, his marriage breaks down between the second and third movies. His hung-over and depressed condition in the third is directly stated to be a product of Holly leaving him, while in the fourth, he has the entire afore-qouted speech about how alienated he is from his loved ones, and how useless being considered a hero is when compared.
Love Cannot Overcome: John and Holly clearly care about each other, but their marriage is already straines in the first movie. While Die Hard ends with them back together, ultimately their relationship can't survive John's Chronic Hero Syndrome. Before movie three Holly leaves John, and by movie four they're long divorced.
Which makes a lot of sense. We see later that he can do a spot on American accent, which shows that he has a talent for accents and English. As he studied in England, he probably took on a perfect English, the parts of German getting through is the fact that he has been working with a large group of fellow Germans for a while now.
Western Terrorist: Subverted, his group use this as a cover for committing straightforward crimes.
Karmic Death: Sending a plane full of innocents to their deaths is pretty unforgivable. So it's only fitting that he and his mooks are blown up on a plane.
Knight of Cerebus: Not that the film wasn't already serious, but even Hans Gruber didn't murder a planeful of people just to prove a point. That Stuart managed this despite John's best attempts (and his No-Holds-Barred Beatdown, below) arguably qualify him for Hero-Killer status.
Bait the Dog: Double Subverred. He initially seems to be another Obstructive Bureaucrat only for him to insult Lorenzo and hits it off with McClane and seems to be becoming McClane’s sidekick for the film. Then it turns out that he’s working with Stuart.
Avenging the Villain: He may not like Hans, but that does not mean he lacks basic brotherly love for him: "There's a difference between not liking your brother and not caring when some dumb Irish flatfoot drops him out a window."
Chronic Backstabbing Disorder: Simon betrays his Middle Eastern clients by trying to keep the gold instead of blowing it up and then tries to maximise his share. He keeps at least some of his accomplices in the dark about the ultimate fate of the gold, and then kills them when they find out. In the alternate ending, he's killed his girlfriend as well a few months after the movie's over.
Even Evil Has Standards: In spite of the money at stake, he will not murder children in cold blood for it. After all, "I'm a soldier, not a monster...though I sometimes work for monsters."
Hoist by His Own Petard: He gave McClane a bottle of aspirin, which gave him the location of their hideout in the climax.
Large Ham: Like Scar in the previous year, Jeremy Irons seems like he has a lot of fun playing charming and devious villains.
Noble Demon: The kind of leader a band of warriors have is reflected in their behavior, for unlike most moustache-twirling one-dimensional villains, Simon's men actually go out of their way to make sure children will not be hurt in their operations, and actually bother to mourn the losses of their brothers before rejoicing in their ill-gotten money. Goes hand-in-hand with Even Evil Has Standards above.
Not So Different: Both he and McClane are suffering from headaches (no thanks to each other) throughout the movie.
The Voiceless: The original ending to the movie suggests she may be mute, but in the final cut she does yell when shooting at McClane.
She was originally supposed to have a speaking part in the film; however, it was decided that her character would be silent, since it made her appear much more imposing and lethal. This makes the scene where she slices one of the Federal Reserve guards to death much more powerful.
Smug Snake: He believes himself to be on a higher intellectual plane then everyone else, particularly McClane. Unlike the supremely magnificent Gruber brothers of the coldly efficient Colonel Stuart, however, his attempts at improvisation seem to be more desperation than mere adjustments to his plans, and his attempts to impose himself threateningly don't seem to carry the same weight. It doesn't help that he's an obnoxious, pretty-boyInsufferable Genius.
Well-Intentioned Extremist: At least he claims to be. The fact that he's "getting paid for his work" kind of makes this hard to believe, though.