One of the nastier ways to kill a character that tends to show up in a lot of Slasher Movies. Quite simply, the killer takes a knife or other blade (or if the killer is a monster, its claws will do quite nicely) and slashes the victim's belly open (often from groin to sternum), usually resulting in the poor unfortunate's insides spilling out.
If the gutting is self-inflicted and a matter of honor, see Seppuku.
Related to Half the Man He Used to Be. If the victim is pregnant, a Traumatic C-Section may occur.
While gutting does not necessarily lead to death, the good majority of the examples are deadly, so Beware The Spoilers!
One Nick Fury miniseries concludes in a two-sided No-Holds-Barred Beatdown between him and an ex-Soviet colonel and culminated in Nick slashing his opponent's abdomen open and strangling him with his own guts.
Minor slasher villain Speed Freek tries this on The Incredible Hulk once. The Hulk has no problem holding his guts in, but then his skin heals over his hand...
Scream provides the trope name (where the killer threatens to gut Casey like a fish if she hangs up on him again) and two examples right in the opening scene, which has both Casey and her boyfriend Steve being murdered this way, with Casey's body being hung from a tree for extra nasty points.
It happens again quite explicitly with Olivia in Scream 4. A deleted scene shows that Jenny and Marnie suffered the same fate.
Near the beginning of Jurassic Park, Dr. Grant gives an impromptu lecture about the possible links in ancestry between the velociraptor and birds while at an archeological dig site. He gets interrupted by an obnoxious kid, who quips the raptor, "looks like a big turkey." So Grant, much to the amusement of his students, teaches the boy a lesson in respect by explaining exactly how that "turkey" hunted and killed its prey. Grant shows him the raptor's middle toe claw and swipes it across the boy's belly then down his midsection to illustrate the cutting motion it used to spill the victim's intestines; finishing his tutorial by telling him that, "The point is, you are alive when it starts to eat you."
Hannibal from Hannibal cuts a man open then throws him out a window with a noose around his neck. His intestines fall out and splatter on the ground. A little earlier in the movie, Hannibal had described how this same method of execution was used on the person's ancestor.
One-Eye executes a man like this in Valhalla Rising. He slices him open, pulls his innards out with his bare hands and throws them to the floor at the man's feet as he dies.
In Jurassic Park, Dennis Nedry dies in this fashion when he has the misfortune of encountering a Dilophosaurus, nicknamed a "spitter" among fans of the films. It blinds him by spitting into his eyes, then rips open his midsection, similar to the way Grant described in the film version. Likewise, Nedry was alive when it began to eat him. His final thought was to pray for a quick end.
In the second book of the Sword of Truth series, Zedd heals a woman who "held her guts from spilling out of a ripping wound in her abdomen."
Many Stephen King books contain this. He especially likes to have characters step on a loop of their own intestines.
An off-screen, er, off-page example is described in the first act of Macbeth; the titular character is said to have confronted MacDonwald and in the end, "he unseam'd him from the nave to the chops / And fix'd his head upon our battlements." How lovely.
In Seeking Who He May Devour, by Fred Vargas, it is mentioned that according to the lore, werewolves are hairless when in human form because all their hairs are inside their bodies ; cutting them open "from the throat to the balls" to check for hairs is the best way to identify them. When Massart, the asocial, hairless butcher is suspected of actually being the werewolf that killed dozens of sheep and Suzanne, it seems that Soliman and the Veilleux really want to do that to him.
In The Borgias episode "The Choice", Cesare takes brutal vengeance upon Giovanni Sforza for proving very ungallant toward his sister Lucrezia, who has had her marriage to Sforza annulled because of this and other jerkassery, by means of this trope.
One of the possible critical hits you can inflict in Warhammer Fantasy Roleplay — also an easy way to kill yourself when fighting a troll (they are the local staple of Extreme Omnivore with metabolism to match, so gutting one will get you covered in Hollywood Acid with nasty results).