24: At the end of the first season, when the Big Bad staying at an accomplice's house Jack Bauer takes the daughter of the host hostage and demand that everyone drop their guns. Victor Drazen merely smiles and shoots her. Her father is understandably upset about this, but at this point he has outlived his usefulness.
Angel: There was a variation in which Kate Lockley staked the hostage. She angled the stake upwards and rammed it through Angel's stomach so as to be fatal to Angel's captor while merely very painful to Angel. Angel didn't realise she was taking care not to kill him.
Angel: You missed.
Kate Lockley: No I didn't.
Implied as a threat in the short-lived series, Boomtown. A corrupt cop is exposed and takes the widely-hated internal affairs investigator hostage. One of the cops points this out and mentions that nobody would be particularly troubled in the investigator got shot in a firefight.
Burn Notice: In Season 4 at the end of the midseason cliffhanger Michael goes to confront Barrett. He is being held hostage by one of Barrett's men and Jesse shoots through Micheal to kill the man. The shot and following car crash put Micheal in the hospital. He is suffering from his injuries for several episodes of season 4.5.
Sam and Fi think, at first, that Jesse deliberately shot Michael, as he has recently found out that Michael is the one who accidentally got him burned. It's possible it may have been a little of that.
Charmed: In the episode "Which Prue Is It, Anyway?", when Prue's duplicate tries to make the warlock of the week surrender his weapon by holding his ally hostage. He instead kills his ally before killing the Prue duplicate.
Invoked by Piper in "The Day the Magic Died." She's in labor, a demon has a knife to her throat, and Phoebe is reluctant to vanquish him. Piper, desperate to save her baby, begins to tell Phoebe to forget about her and vanquish him to save the baby, or as Piper so delicately put it, "Phoebe, if you love me, you will send this crazy bastard straight to hell!"
Chuck: Bryce did it when Chuck was being held hostage. He did make sure Chuck was wearing a Bullet Proof Vest first, though... by asking him in Klingon.
A variation in Defiance: The hostage is a wanted criminal, the hostage taker is Nolan's old army buddy turned bounty hunter. Nolan settles their stand-off over who gets custody of the bad guy by shooting him in the head. His buddy is not amused.
Demons: In the first episode, the protagonist is instructed to shoot his (not) girlfriend with magic ammunition, which he is told will only bruise her at worst, but will disintegrate the monster holding her captive. He complies, and after that, she's pissed at how little hesitation it took for him to shoot.
The Equalizer: Robert McCall is holding a gun to the head of a Double Agent, and offers to swap him for one of his men being held prisoner by a KGB cell. The head of the cell replies, "Why don't we dispense with the formalities" and shoots the double agent dead. Caught without his human shield, McCall is then taken prisoner too.
For the Term of His Natural Life: In this Australian mini-series, an attempt by convicts to escape ends with a sergeant being held hostage, facing a small cannon aimed by his fellow marines. The sergeant orders them to light the fuse and kill them all. Realising he's not bluffing, the convicts are forced to surrender.
Fringe: In the episode "Entrada" Peter shot hostage held by a Fauxlivia. That's because he figured out (s)he was a shape-shifter.
In the first episode of Hostages, Dylan Macdermott's character does this. The hostage was actually the hostage taker, having switched clothes with the hostage.
Justified: In season 4 Constable Bob Sweeney ends up stabbing a hostage in the foot with his knife which surprised everyone so much that Raylan was able to disarm the hostage taker. It is unclear whether this was on purpose or whether he stabbed the wrong foot since Bob just suffered a Groin Attack and was not seeing straight. This was a deliberate Shout-Out to Speed since series executive producer Graham Yost was also the screenwriter for Speed.
A shot of the perp's left shoe next to the hostage's right makes it look as if he might have chosen to stab the hostage's foot because she was wearing thinner shoes.
Law & Order: A totally horrible example comes when an escaped convict holds a classroom full of students before anything can be done, he shoots all of the hostages in the room. His reason "Why not".
Leverage: The leader of a gang of Russian gangsters intimates that he'd do it in one episode after Eliot uses one of his men as a human shield:
Hardison: You going to shoot through your man?
Russian Gangster: To be honest with you, I never liked him anyway.
Lost: Variant: the episode "Enter 77". Kate and Sayid are holding Mrs. Klugh, who responds by ordering Mikhail to shoot her dead, which he does.
NCIS: Agent Lee got Gibbs to shoot through her to take out the Weatherman.
Person of Interest: In the episode "Most Likely To...", Reese throws a plate at the hostage's leg and then a can of sloppy joe sauce at the hostage taker's head.
Revolution: Possibly Dixon's intent when he shoots at Monroe and kills Emma, disregarding Miles' protestations.
Rizzoli & Isles: Played with in a particularly nasty fashion. Since it's the Cliffhanger season finale, spoilered: Jane herself is the hostage. She is determined not to let her Corrupt Cop captor escape. She grabs his gun and shoots through herself to kill him. Black screen, end credits. To be continued.
Spooks: Where Ros Myers shoots through fellow officer Jo to kill a terrorist. Jo dies too.
Stargate Atlantis: Genii commander Colya, after being forced to abandon Atlantis, takes Weir hostage and tries to goad Sheppard into shooting them both. Unfortunately for him, the Atlantis team has much more accurate guns, and Sheppard calmly puts a bullet right through Colya's shoulder.
Star Trek: Enterprise: During a shoot-out on a Wild West planet, T'Pol gets a six-shooter put to her head. Reed shrugs, shoots her, then the hostage taker while he's still gaping at Reed's apparently ruthless action. His phase pistol is set on stun.
Oddly enough, hostage taking tends to work in Star Trek, despite the characters carrying Non-Lethal K.O. weapons, thus making the logical response shooting them both.