One of the more peculiarly popular setting aesthetics: Something resembling the American West from the years 1865 (the end of the Civil War) to 1914 (the beginning of World War 1), but generally limited to before 1894 (when the U.S. Census Bureau announced that the frontier was closed). The genre actually was actually established as early as 1903, with The Great Train Robbery, if not earlier.
The thing is, for most of the 20th century, the historic "Wild West" was the logical place to set what we now call an "Action" movie, for several reasons, even if the historical west wasn't actually all that violent or crime ridden. The genre was very influential, and riffs on the Western in a different setting followed in the 1950s onwards.
Just about every genre you can imagine has had either a Western version or equivalent, including, but not limited to: Romance, Murder Mystery (Hec Ramsey), Horror (Curse of the Undead), Science Fiction (Cowboys and Aliens), Spy Thriller (The Wild Wild West), Musical (Oklahoma), Superheros (Lone Ranger), Crime, Modern Fantasy (aka "Weird West"), and War (usually against Indians, which, well, see below under trappings).
The first were probably either the Space Western, or the Samurai Western, depending on how you count. The (1950s made) Samurai films of Akira Kurosawa were very western inflected, and several wound up being remade as traditional Westerns ("A Fistful of Dollars" and "The Magnificent Seven", among many others), which means the Samurai Western has claim of priority in film. On the other hand, the sci-fi magazines and comics of the pulp era loved raygun westerns because they were easy to write and advertise, but since Science Fiction is expensive to film, the first cited example is either the initial pitch for Star Trek (which Gene Roddenberry described as "Wagon Train to the stars"), or 1977's Star Wars. That being said, Horror-themed works set in the "old West" period have a long history as well, with some "Horror Western" films dating back to the 1930s.
There are plenty of trappings that will get a work not set in North America west of the Mississippi River between the years 1865 and 1914 called "Western"-adjacent. The more of the following you have, and the more direct the equivalents of thereof, the more likely you are to be called a "Space Western", "Fantasy Western", "Weird Western", or what have you.
- Very low population density. The most distinguishing feature of the historic West, there were vast ranges of territory where the nearest person could be miles away, which had several implications:
- The Law was mainly limited to towns, which were frequently quite far from one another if they weren't on a train-line. Thus, a Sheriff or Rancher, if he couldn't find local support, was more or less on his own.
- As an indirect consequence of the above, Bandits.
- If the work doesn't center around a larger conflict, expect either bandits or "evil banker" types employing them as the main bad-guys.
- Drifters; that is, men who wander from town to town; they may be traveling somewhere in particular, but for now, but as far as this town (and story) is concerned, they're just passing through.
- In particular, men looking for work and/or opportunities, cowboys who were driving their herd to market, or gamblers looking for new clientelle would historically not have raised the slightest eyebrow.
- Handguns (particularly Revolvers and concealed weapons) and Longguns (particularly shotguns) in places where openly wielding a weapon is allowed (notably, stagecoaches frequently had a guy holding a shotgun in case bandits showed up).
- Quickdraw shooting.
- If the rating allows, prostitutes as the only female company available.
- Bounty Hunters.
- Sand and dirt. (While the actual American West can be fairly green, particularly in the mountains, most people picture a lot of dirt when they picture a Western.)
- Cows. Cattle ranching was one of the main businesses of the historical period covered by the Western, and so "Cowboys" (as the men responsible for herding cows were called) were frequently cast as either protagonists or supporting characters in Westerns.
- Horses, with a side option for donkeys and mules. Historically, the only way of getting around besides the railroad or stagecoach was a horse.
- The main form of farming being animal related is also a frequent feature.
- Railroads. In particular, somebody arriving at a station meeting a "welcoming" committee (who may try to kill him or run him out of town) is a common scene in both direct Westerns and Western-inflected works.
- More rare in post-1960 Westerns: Native Americans.
- Historically-set Westerns have plenty of American Indians, historically. It's just that, by the 1960s, most writers decided it was a better idea to center around subjects that weren't so likely to be read as making their protagonists "the real bad guys". Thus, most post-1970 westerns center purely on White vs. White conflict, or have protagonists who are sympathetic with the Indians, with a smattering of works centered on Black characters (most notably Blazing Saddles). (Historically speaking, there were plenty of black cowboys, but this was ignored by most writers and producers historically, and frequently still is in the present day.)
- Bonus points if the setting has both "friendly trader" and "hostile barbarian" tribes of Native American equivalents (see: Jawas and Tuskan Raiders in Star Wars).
- There are a lot of Mexico-set Western media, particularly among those Westerns made since the mid 1960s. Mexico's very colorful history with civil wars, bandit-revolutionaries and general political strife mean that if an author is going political or post-1894, Mexico is a good place to set a large chunk of your story.
- For "Western-inflected" works, if you have a place that's somewhat nearby, and going through violent revolution (or on the verge of one), you may be in pseudo-Mexico.
Oh, you're wondering what /tg/ relevance this has? Well, just to start with, with RPGs we have:
- Boot Hill
- Dogs in the Vineyard
- Pathfinder's Gunslinger class.
- Werewolf: The Wild West.
- That RPG based on Firefly/Serenity.
- And plenty of others.
Then there are actual board games set in the period (MANY railroad games, just to start with.)
More general influence
In addition to all the above, we could very well argue that without the Western, we never would have had Dungeons & Dragons, which, despite what Historical Fantasy nuts may say, began its existence this strange hodge-podge of common Western tropes in a quasi-Medieval Europe backdrop and infused with Sword & Sorcery, Classical Mythology, European Mythology, Tolkien, and whatever elements of pop-culture from the 60s-80s that TSR felt like including. It even got a literal cowboy god, rolled up by one of Gygax's friends and a lifelong Western aficionado in the second-ever session of D&D. Even to this day, the "standard fantasy setting" is more like a Western set in a faux-European countryside than anything else.
Genre variants we have articles on
- Works set later than 1894 usually center around people who can't let go of a way of life that's no longer possible--for example, Red Dead Redemption 1 or The Shootist, John Wayne's last movie.
- The era was still in living memory, the most common forms of action (gunfights, horse-riding and semiskilled fistfighting) were all easy to fake, and Hollywood was conveniently located to a lot of filming locations that resembled a lot of other places in the American West, there was plenty of well-documented low-level conflict to base your fiction upon, there was also a lot of existing pulp fiction about the era (some of it written during the period in question), and the details (props and costumes) being fairly cheap to build or buy your own version of.
- It cannot be understated how much easier having two sets of cliches to draw from makes things for writers.
- Admittedly, the most notable example (Phantom Empire, the first Gene Autry film--well, actually a serial, but that's not that important) took place in the then "present day" of the 1930s, but was still counted as a Western (if a weird one) by audiences of the day