Time Travel can cause a lot of damage. You could run into the Butterfly of Doom, leave behind a Timeline-Altering MacGuffin, try and bump off Hitler or create a Temporal Paradox. Therefore, in any society where Time Machines are easily accessible, deliberately altering time will be a crime. In addition, there may be people, most likely a police force or The Men in Black, who fight those who violate the sanctity of time.
Of course, not all who police time are part of an official organization. In a setting where time travel is not easily accessible, there may be no laws to cover altering the timeline. Time Police in this case is any individual or group that takes it upon themselves to make sure that time plays out the way it's "supposed" to (although this brings up the question of what "supposed to" means. What's to say Hitler ''should'' have won World War II, and a time traveler has altered it?) and keeps the timestream free of paradoxes. They may or may not be supernatural in origin, in this case.
Although Time Police are usually intended to be Lawful Neutral, with their only obligation being to keeping time clean, so to speak, they will often fight on the side of good anyway. Somebody ought to check the screening process. Although there's an increasing deconstructive trend to make them Knights Templar willing to do anything to preserve the timeline they want. Sometimes they might serve as a Weirdness Search and Rescue (although the latter characterisation might still be applied, with the one who helps the protagonists being the equivalent of a Cowboy Cop).
Oddly, if they're introduced in a long-running science fiction franchise, the question of where (when?) they were all the other dozens of times that time got messed up is barely handwaved if mentioned at all.
Also, Time Police covers other activities besides hunting down reckless or malevolent time-travelers. They spend most of their time protecting Adolf Hitler from being assassinated. (Lawful Neutral, remember?)
If there is no such group in a setting it may come down to the heroes to take care of the same. This can prove to be difficult. Time Police are very common in a world with Casual Time Travel.
Sister trope to Clock Roaches. While the Time Police are people, and therefore fallible and have agendas, who happen to use Time Travel technology to do what they see as their duty, Clock Roaches are animals, often non-sentient, who are inherently able to attack time travelers. In contrast to Time Police, they also happen to be Nigh Invulnerable, Eldritch Abominations, and/or Have Reserves. Either way, though, they both serve the same purpose as tropes: to provide an unambiguous in-universe reason why trying to change the past is a very bad idea.
- Subverted in Meet the Robinsons. Lewis is reluctant to believe that Wilbur is a time traveler working for the "Time Continuum Task Force," especially when he notices that his "badge" is a coupon for a tanning salon. He's then surprised to learn that, while the police angle was a lie, Wilbur really does have a Time Machine and comes from a thirty years in the future.
- Cassie in Frequently Asked Questions About Time Travel belongs to one of these organizations.
- The secret time travel agency in Predestination. Its purpose to prevent crimes before they can happen. Or as Robertson puts it, the agency is "reshaping wrongdoings".
- Timecop is probably the Trope Codifier. Jean-Claude Van Damme is part of an agency who travel to the past to heroically prevent time travel from being abused!
- TIME, the from the Gamebook Falcon, the "Temporal Investigative and Monitoring Executive".
- In a Gamebook based on G.I. Joe: A Real American Hero, the villains have made a working time machine, and the Joes can make funky helmets and pretend to be Time Police coming to arrest them.
- In Chrononauts, the Time Repair Agency functions as this. A player who has 10 cards in their hand (one of the three ways to win the game) is made a new Agent in-game due to their skill at fixing paradoxes.
- All PCs in the time-travel RPG Continuum have this as one of their basic duties, although the Foxhorn Fraternity is the one specifically devoted to the task of rooting out Narcissists (time-criminals). Note that the RPG specifically mocks and derides the trope of the "Time Police" as a bureaucratic organization, and describes this as a misconception caused by our 20th-century prejudices. Keeping the timestream clean is everyone's responsibility in the Continuum.
- Dungeons & Dragons: This is the job of the Quaruts, one the types of Inevitables — living mechanical beings hailing from Mechanus, the plane of Law, whose purpose is to uphold the sanctity of law in the multiverse. Quaruts are one of the most powerful kinds, and they are specifically meant to prevent anyone from altering the past and, through that, risking causing irreparable damage to causality.
- The Sidereals and other employees of the Bureau of Destiny in Exalted fill this role to some extent. Even if they exist in a universe where time travel is technically impossible, there is still a notoriously unstable Loom of Fate that has to be protected from disturbing elements (such as other Exalted or the creepy things living outside Creation).
- The Guardians of Forever in Genius: The Transgression. The Terminals filled the role before they were removed from the timeline. In something of a subversion, said Guardians are incredibly overworked, paranoid and looking for help, and also fractured and corrupt — many have gone renegade. At least the current timeline seems relatively stable... for now.
- The GUMSHOE system has TimeWatch, where agents from the eponymous organization investigate sudden changes to the time stream and negotiate various time travel dilemmas such as paradoxes.
- The Infinity Patrol (and its elite division ISWAT) from the default GURPS setting is partially tasked with policing alternate timelines. Unlike most time cops they are far from neutral as their main objective is to protect the interests of Homeline.
- GURPS also has an actual time-travel version in Project Timepiece, the default setting in GURPS Time Travel for Third Edition and an alternative setting in Fourth Edition’s GURPS Infinite Worlds. Timepiece personnel battle against agents from an alternate present known as Stopwatch; the two are presented as equally possible with the actions of each determining which one becomes real.
- Pathfinder: One of the types of outer dragons, a group of dragon species tied to wide-reaching cosmic concepts, is the time dragon. They see themselves as guardians of the integrity of time, and protect the universe against those who would interfere with the natural order of the timeline.
- In Savage World's "TimeZero, the PCs play Time Police agents.
- Warhammer 40,000, given that the only means of interstellar travel goes through essentially hell, and people have been known to reach their destinations before they left, has mentions of a subsection of the Inquisition devoted to this, the Ordo Chronos. Who all mysteriously disappeared at the same time. And who all may reappear somewhen.
- In the Yu-Gi-Oh! card game, there's this guy. He's just what his name implies.
- Used in this Bahala Na strip.
- In a brief arc in League of Super Redundant Heroes, a guy with the ability to teleport uses his power to pretend to be from the future and scare people into stopping what their doing. His pranks finally stop when his intended target is a real undercover Time Policeman who arrests him for "conspiracy to commit severe continuity disruption".
- PepsiaPhobia: If this page of possibly-canon strips is to believed, then Philia is not an ancient Amazon, but actually an undercover Time Cop posing as an Amazon. Even better, she's Phobia's Kid from the Future, an Amazon and a Time Cop.
- Deep Time from Starslip serve both as a parody as well as a Deconstruction. Originally, they appear fairly uninvolved with the plot, only hunting rogue time travelers, but eventually they get into a jurisdictional dispute with the present over a time machine. This leads to a war in which the Future battles the Past, and Deep Time can't do anything without erasing their own existence, while mankind's present's government tries to beat them by banning time travel research, but continue it in secret anyway, leading to Deep Time's existence. Eventually, they erase the entire timeline and start over to ensure their own existence comes to pass, though the past would have won for want of a spork.
- The Time Line Authority in TRU-Life Adventures.
- Times Like This: Agent Keith Scott is a one-man Time Police, keeping Cassie and her friends out of temporal trouble.
- The Thrilling Adventure Hour gives us two versions of this with "Amelia Earhart Fearless Flyer" and "The Cross-Time Adventures of Colonel Tick-Tock." Amelia flies through time trying to stop time traveling Nazis who want to Make Wrong What Once Went Right, while Colonel Tick-Tock does the same for more general threats to the timeline by the order of Queen Victoria.
- One episode of Dr. Zitbag's Transylvania Pet Shop involved the Time Police.
- Futurama had the Vice Presidential Action Rangers in the What If? episode, a "group of top nerds" tasked, by the U.S. constitution, to protect the space time continuum from disruptions. It consisted of Al Gore, Stephen Hawking, Nichelle Nicols, Gary Gygax, and Deep Blue. Fry lampshades the odd assortment.
Fry: I thought your job was to cast the tie-breaking vote in the Senate.
Al Gore: And protecting the time-space continuum. Read your constitution.
- The Adventures in History retool of Gadget Boy & Heather had the premise of Gadget Boy and Heather going back in time to prevent Spydra and her lackeys from altering history.
- Gravity Falls has Blendin Blandin, who was sent to fix temporal anomalies, and is thus more of a Time Mechanic. When his appearance actually causes those anomalies, actual Time Cops show up to arrest him.
- Koala Man: "Time Bobbies" arrest anyone who breaks the "Red Hot Rule" altering the past due to Australia being literally fifteen hours ahead of America.
- Milo Murphy's Law has the Bureau of Time Travel, whose main focus seems to be using time travel to improve the future while preserving the timeline, such as sending agents back in time to find a cure for the common cold or prevent the extinction of pistachios.
- The Time Cops in Rick and Morty are a race of aliens resembling testicles from the fourth dimension who regulate the space-time continuum. In their first appearance one of them tries to arrest Rick, Morty, and Summer for possessing a time crystal and later on the same one and his partner wipe out a race of sapient snakes by killing their ancestor after Rick gives them time travel technology.
- While there is a group called the Time Police in Superjail!, they don't do anything that fits this trope. The Warden's "time-crimes" are not related to time-travel at all, and instead are from him making a decision that would snowball into Superjail waging war on the rest of the world, destroying the planet's ecosystem and enslaving all of the Earth's population that don't die trying to fight him.
- Time Squad is about a time cop, his robot servant, and an orphan history expert who venture throughout history to keep time continuity straight. Examples include forcing Ludwig van Beethoven to give up his Professional Wrestling career to resume composing, and getting the pirate Blackbeard to trade conservationism for buccaneering.
- On Time Warp Trio time travelers are responsible for making sure other time travelers like the series Big Bad don't screw up history. It's mostly informal, but they have Time Agents posted at certain at risk times/places, and they do travel back specifically to stop him at least a few times.
- Uncle Grandpa episode "1992 Called" sees the main character call in the Time Police (named as such) himself to resolve an otherwise untenable situation with Christopher Columbus refusing to return a pair of time-displaced parachute pants.