In the center of the chest (and tilted slightly to the left) lies the heart: an extremely important muscle that happens to be the sole thing responsible for moving blood throughout the entire body. As such, causing severe enough damage to it is one of the surest ways to kill someone. In real life, police and military personnel are trained to fire at the center of mass (read: chest/heart) specifically for this reason: it incapacitates or kills a target much more consistently than aiming for extremities.
Along with throat-slitting, decapitation, and shots to the head, this is one of the classical ways of killing someone in media. Generally speaking, any character that takes a direct hit to the heart will either die instantly or drop dead after just a few seconds.
This trope can easily overlap with Impaled with Extreme Prejudice or Inertial Impalement. Vampires, which are otherwise immortal, can often be killed anyway by impaling them through the heart with a wooden stake: a depiction so common that it's a trope in its own right. If the attack actually removes the heart from the body, the victim will often see their own heart, still visibly beating before they die.
Because filmmakers aren't necessarily familiar with anatomy, on occasion a wound will treated as damaging the heart even though it's clearly not in the center of the chest. Instead, they place the wound beneath the left shoulder, where the heartbeat can be felt. That would be the aortic pulse, not the heart itself. That said, almost any penetrating wound to the thorax has a high chance of being fatal due to the number of important organs and (more significantly) major arteries and veins. The heart itself can also be affected by shock damage even if the injury itself misses, so there's some Truth in Television to this, as well.
Since this is a Death Trope, EXPECT UNMARKED SPOILERS!!!
- Red Sprite: Tatsu kills Shepherd by stabbing him in the heart with his sword, but only penetrating up to the pericardium so he can electrocute it with his Thundercore powers. The resulting convulsions cause the heart to implode and crush itself.
- In Rabbit of the Moon, Bell finishes off the minotaur that killed him by reaching into its chest and ripping out its Magic Stone.
- Dungeon Keeper Ami: Zarekos temporarily kills Wemos - a vampire - by attacking his heart:
cracked-open ribcage, grabbed the beating heart, and plucked it from its exposed perch in a shower of blood. Immediately, the separated organ and its owner dissolved
- Assault on Precinct 13 (1976): In infamous scene, a member of the Street Thunder gang kills a little girl by shooting her in the middle of her chest at point-blank range.
- Batman v Superman: Dawn of Justice: Both Superman and Doomsday are stabbed through the heart, simultaneously. Superman got better.
- Equilibrium: John Preston kills DuPont with a single gunshot to the heart.
- Terminator Salvation: Marcus has a human heart despite being a Hollywood Cyborg. Towards the ends of the film, a Terminator attempts to destroy his heart because it's his only vulnerable spot.
- Smokin' Aces 2: Assassins' Ball: Katlyn Tremor is shot twice in the heart, and finished off with a shot to the head.
- Frozen: When Anna was hit in the head by one of Elsa's ice beams, she was knocked out and got a permanent white hair streak. The troll shaman manages to heal her, but warns that a similar strike to the heart would lead to a painful, slow, and inevitable transformation into solid ice that can only be reverted by "an Act of True Love."
- Star Trek VI: The Undiscovered Country: The Klingon Chancellor Gorkon is assassinated via phaser shot to the center mass.
- Star Trek: The Original Series: In A Private Little War, Spock is shot through the center mass by revolutionaries on planet Neural. He only survived because his Vulcan heart is located where the Human liver is.
- Star Trek: The Next Generation: Captain Picard has an artificial heart as a result of an incident in his youth, he proudly antagonized a Nausican, who then stabbed him through the heart. Since then, he's been a much more mellow individual.
- Star Trek: Deep Space Nine: After overhearing Ziyal's confession of freeing war prisoners, Damar summarily executes her by shooting her in the heart with a phaser.
- The Twilight Zone (1985): In "The Toys of Caliban", Toby Ross accidentally kills his mother Mary when he removes her heart from her chest using his ability to manifest anything from a picture. He had seen a diagram of a heart in a magazine and wanted to know how it worked.
- Drawn to Life: To defeat the Giant Robosa, The Hero must first take out its mechanical eyes; when that's done, you must destroy their giant mechanical heart. Fittingly, it's the most heavily guarded part of the robot's inner body, but is also exposed enough to allow for constant attack.
- Kid Icarus: Uprising: While being forced to travel inside of Hades after being eaten, Pit has a run in with the Lord of the Underworld's heart which serves as the boss for the chapter. The heart actually explodes upon being destroyed... but Hades ends up being no worse for wear despite his heart having literally blown up inside his chest.
Hades: That really hurt. But hey. At least I'm not dead!
- In Red Orchestra, a gunshot to the center of the chest is a One-Hit Kill with a unique kill icon, just like a headshot.
- Super Mario World 2: Yoshi's Island: The boss of World 5's fortress, Sluggy the Unshaven, is a giant Sluggy whose weak point is his heart. Although initially protected by his gelatinous body, it becomes vulnerable after hitting him with several eggs. After that, a few direct hits to his heart will defeat him.
- Transistor: Red kills the Spine by walking inside and destroying its heart.
- Heavy Rain: In one of Jayden's possible deaths, he's killed by having a katana run through his chest. The Origami Killer can also die this way, via gunshot to the heart.
- In Lugaru, Turner always throws his knives at the heart.
- Fate/stay night: In one of the routes, Gilgamesh kills Illya by ripping her heart out. In another, he thrusts a sword through her heart.
- Lancer's Noble Phantasm has his spear killing his target by gorging their heart. Even if the target manages to avoid the hit, the spear will control time to make sure the hit happens.