The Trope Namer comes from the above quote from Speed, obviously. Shortly after that conversation, the situation describes happens, with Harry as the hostage. Jack, true to his word (and at Harry's insistence), shoots him in the leg, much to the hostage-taker's surprise (Harry's too, as he didn't think Jack would actually do it). The villain learns from his experiences in their next confrontation and straps explosives to Jack's love interest, while holding a Dead-Mans Switch, making this tactic unusable.
At the climax of 2007's Live Free or Die Hard, McClane is himself the hostage he shoots to kill the movie's Big Bad, firing through his own shoulder to get the villain in the heart. He had already been shot in the shoulder once, and the Big Bad was holding the gun to the wound at the time to torture him.
The movie Hard Boiledhas the hostage shoot himself to hit the villain, also allowing Yuen to finish the villain off with a shot to the head. This scene may in fact have been the inspiration of similar action movie scenes made later.
In Another Forty Hours, Eddie Murphy is taken hostage, and with his characteristically big mouth, asks the cop to "Just shoot me!" Which he then does. He doesn't even bother aiming for the legs.
In Shark Tale, Oscar attempts to fake this when the Sharks kidnap his girlfriend by having his "dolphin" partner pretend to eat her right on the spot (he grabs her in his mouth, but doesn't swallow) on his order to show that he didn't care. Fails, as the "dolphin" is a vegetarian shark who is repulsed by the simple taste of fish. He spits her out along with the contents of his various lunches.
From the 1994 film of The Shadow, a villainous variant:
Opium Farmer:(having just taken Ying Ko's accountant hostage) Even your men are not marksman enough to shoot around him! Ying Ko: You're right. (to the accountant) Wu, you're a wonderful friend. You're like a father to me. Accountant: Thank you, Ying Ko. Ying Ko:(to his marksmen) Shoot through him.
Roman fakes doing this to one of his own hostages earlier in the movie in order to convince the police he's serious about his demands.
In The Usual Suspects, according to Verbal, Keyser Soze once saw his raped wife and children held at knifepoint by Hungarian gangsters. They kill one kid to let him know they're not fooling around. He kills the other kid, and his wife, and all but one Hungarian, to let them know that he isn't either.
Subverted in the original RoboCop (1987), where the cyborg's first patrol ends in him shooting through the skirt of the attempted rape victim to hit the knife-wielding thug behind her right on his groin.
In The Film of the SeriesS.W.A.T., Brian Gamble solves the hostage problem by shooting the hostage taker through the hostage's shoulder. (He was actually trying for a headshot on the hostage taker, but the target was moving.) Predictably, this does not sit well with his hierarchy (or the hostage, for that matter), leading to both him and his partner Jim Street being kicked off the team.
In the opening montage of Soldier, Kurt Russell's character, an emotionless super-soldier, shoot a civilian to hit the enemy target behind in a shooting range. Later in combat, he shoots a civilian dead being used as a human shield by the enemy.
The ending of The Deaths of Ian Stone. Medea tries to save herself by using Jenny as a shield, but Ian runs them both through, then hits the Reset Button and reunites with Jenny.
Subverted in the Hyakujuu Sentai Gaoranger film Fire Mountain Howls, GaoGod looks like he's about to do this to GaoKnight to hit Hades Org. Despite everyone, even the Gaoranger, assuming he's trying to do this, being a God, he bends the arrow around GaoKnight's head through Hades Org's.
In both versions of 3:10 to Yuma, the plot gets started by Ben Wade's gang robbing a wagon (a stagecoach in the original, while it is an armed carriage in the remake). After overtaking the wagon, one man attempts to hold a member of the gang hostage, only for Wade to shoot the outlaw and then the hostage-taker.
In Night of the Comet, the protagonists are captured by a gang of quasi-zombified stockboys. One of the girls grabs one of them as a human shield, and the leader casually shoots his own man, for no reason other than to show how little he cared.
In the second Crocodile Dundee movie, the drug lords are trying to find Mick in the bush, so they kidnap Walter both as leverage and as a tracker. Mic shoots Walter in the ear after the drug lord threatens to kill Walter if Mick doesn't come out. It saves Walter's life in the long run as the drug lord thinks Mic doesn't want them to have Walter to track him.
In Taken 2, Bryan tries to use a mook as a shield. His fellow mook guns him down without hesitation before continuing after Bryan.
In The Dark Knight, when the Joker breaks out of his cell and takes Stephens hostage, Stephens tries to convince his fellow officers to do this, since he knew he was stupid enough to walk right into it.
Stephens: It's my own damn fault! Just shoot!
A variation in Half Past Dead: When the bad guys take control of Alcatraz, some guards manage to overpower two random mooks and hold them at gunpoint, demanding the Big Bad to release an important hostage. True to his role, the Big Bad immediately shoots his own mooks, and then shoots the guards. Then the mooks suddenly get back up seemingly unscathed, and the Big Bad casually asks if they got their bulletproof vests on, to which the mooks enthusiastically nods.