More often than not, the Knights of the Round Table are portrayed in plate-and-mail armor with big chargers that didn't get to Western Europe until hundreds of years after these myths supposedly took place. This dates back to Malory.
Knights living in huge stone castles. There were no new stone fortifications built in Britain between the 6th century and the 11th century. Most of the old Roman forts were abandoned, dismantled for their stone, or repurposed. All of the great castles were built following the Norman Conquest.
The Knights of the Round Table themselves, as feudalism had not yet arisen in the Roman-era Britain when the historical Arthur is believed to have lived.
The majority of the anachronisms in the Arthurian mythos came from French poets reading the History of the Kings of Britain by Geoffrey of Monmouth and changing society/technology to coincide with medieval French society/technology.
White's book was, in turn, referenced by Terry Pratchett's story Once and Future, where Mervin, a time traveller stuck in the past, adds to already anachronistic setting of the Arthurian mythos. He ends up re-enacting the King Arthur legend... except for that final twist...
The "courtly love" mythos — including the very existence of Sir Lancelot — and the Grail legends were introduced to the Arthurian legends by remorseless retcon.
The all-time champion of Arthurian anachronism was Wolfram von Eschenbach. Parzival, his version of the Grail Quest, adds sixth century Africans who worship Jupiter and Juno while practicing high medieval courtly love.
Peter David's Knight Life Series of Arthur in the modern era. Percival, who gained immortality by drinking from the Grail cup while healthy, is portrayed as a Moor.
King Arthur Pendragon deserves mention for resolving the Anachronism Stew of the Arthurian legends by having King Arthur's reign magically feature technology advancing at super speed from Dark Ages to high medieval, until history re-asserts itself after the Battle of Camlann.
Justified and lampshaded in A Hard Day's Knight, in which the shiny armor worn by Arthur and his vassals was forged by armorers acting under the explicit instructions of Merlin, who'd peeked into the future to see how later generations of warriors were kitted out. This also explains why Arthur could kick ass on every other military force in 6th century Britain: his guys were more or less invulnerable to the weapons of his rivals.
The film, deliberately. The characters, environments, and vehicles seem to be early 20th century, but fax machines and reel-to-reel car tape decks and carphones seem to be 80s, and Olaf mentions a cell phone in a deleted scene. Given that Poe actually has to feel himself to check, one assumes that giant 80s-style cell phones aren't common at the time.
The books keep the time period as vague as possible, easily taking place any time in the 20th century, and the only real definite is that it takes place in the past but whether it's a hundred years ago or last month, it's never certain.
What with the computer in "The Austere Academy" being small and able to display a picture and may or may not be able to fake photographs, it definitely takes place sometime after the 50s, or at least at a point when computers did not fill a room.
Handler has way too much fun with this. At one point a location (a train station, if I remember correctly) is mentioned to have three shops - one is a computer repair shop. Another is a blacksmith shop. Have fun figuring out what time period those two establishments could coexist in.
Michael Crichton's Eaters Of The Dead is remarkably true to real history, aside from the obviously fictional and fantastic nature of the "Eaters of the Dead" themselves, and the fact that the real ibn Fadlan never traveled all the way up north to help the Vikings fight Neanderthals, given that much of the book is based on a historical figure's travelogue. As a result, it's so much cooler. However there's one minor anachronism... in the basic premise. The plot of the novel is obviously meant to be a "real life" inspiration for Beowulf, a poem that most scholars think was written at least a century before ibn Fadlan lived.
Also used by none other than the poet Homer. The Iliad and The Odyssey were set in AchŠe (MycenŠan-Era Greece), but contain a wild mixture of elements from the Archaic and Classical periods with a few MycenŠan leftovers thrown in for good measure. For example, boar-tooth helmets were MycenŠan, but funeral pyres belong to a later era.
The ancient Irish epic Tßin Bˇ C˙ailnge features chariot warfare, but there is no archaeological evidence that chariots were ever used in Ireland. This suggests that the tale (or parts of it) is very old indeed, dating to the time when the Celts still lived in continental Europe.
Chris Elliot's novel, The Shroud of the Thwacker, set in the 1890s, features gas-powered cellphones, among other things.
One for the Morning Glory, where it is lampshaded as well; when Sir John drinks tea, he wonders whether it is really suitable to be drinking tea, and the Duke dismisses that as a consideration only for those lands that are merely actual.
Gene Wolfe's New Sun series of novels take place a looong way in the future (the techno-fantasy "post-historical" era where Stone-Age Man, the Modern Era, and the Galaxy-Spanning Imperial Era are all lumped together as the "Age of Myth"). The basic technology and society is late medieval. But at some point time travel had been commonplace, so remnants of all eras of history are common - military energy weapons right along with swords, antigravity craft and ox-drawn wagons, sabretooth tigers and starships, electricians organized like a medieval craft guild, medical men just as likely to use genetic engineering as an herbal infusion, etc. One of the appendices even points out that there are three separate levels of technology: the "smith" level (medieval), the "Urth" level (roughly 20th century plus some genetic engineering) and the "stellar" level (highly powerful artifacts that can only be obtained from extraterrestrials.) It's all justified by the fact that the planet has been exhausted of most resources and can no longer sustain a technological society or educate most of its inhabitants, but the old knowledge remains in a few places.
The Aeneid features Aeneas, fleeing the destruction of Troy, landing at Carthage... which wasn't founded until hundreds of years later.
The Mistborn series is built on this. While at first glance it appears to be your standard medieval setting, it turns out there are working pocket watches, gunpowder (though it isn't used), and a knowledge of metallurgy and medicine that rivals our own. Turns out this was intentional: What do you think happens when the world is ruled for a thousand years by an immortal god-emperor who doesn't like change? Said god-emperor, while deliberately stagnating many technological developments, also develops the canning process (metal cans were invented in 1810) and other advancements but keeps them strictly under his own control.
As well, the knowledge of metallurgy is a Justified Trope given that the magic used by the world's nobles is run on specifically mixed metals.
The Bible, especially in some versions/translations, has been known to contain a few anachronisms since often the "books" composing it were written some time after the events were supposed to have taken place. For example: the descriptions of armor, especially that worn by Goliath, in 1 Samuel 17 are typical of Greek armour of the 6th century BC rather than of Philistine armour of the 10th century BC.
All of the Hebrew Bible from Genesis through 2 Kings wasn't written down and in it's final form until around 500 BC or later, so descriptions such as the above would be based on contemporary examples.
George Macdonald Fraser's The Pyrates is a colossal Anachronism Stew, with seventeenth century pirates riding around in catamarans and using face cream. Fraser was a diligent researcher and knew exactly what he was doing, even lampshading it in a few places. It's all more than justified by the fact that the novel is hilarious.
The Princess Bride actually uses the invention of stew to clarify its chronology. Most definitely Rule of Funny and metahumor. William Goldman often states that the time he's talking about is before one thing, but after another — often putting them in ahistorical order, as when he says it's set "before Europe and after America". (Unless he means "after Vespucci's voyages but before the Maastricht Treaty"...)
Secret of the Sixth Magic by Lyndon Hardy has an in-universe example (for another universe's history) — the sorcerer Farnel is said to have lost out in competitions against other illusion-crafters, because his simulations of famous historical events succumbed to Anachronism Stew. Apparently this trope isn't just universal, it's multiversal.
Andrzej Sapkowski (Witcher) intentionally includes some elements of that in his medieval-esque settings, like "genocide" when that word wouldn't have existed yet (to make a point that wars don't really change) or various orders reminiscent of those by Nazi generals to derive the war of any mysticism and allegory and show how seemingly senseless cruelty is justified by tactics.
The Pirates! In An Adventure With Scientists by Gideon Defoe, is set in the 1800's and yet there are things like tap water onboard a pirate ship, crazy golf, after eight mints, and Coco-Pops. It's not as a jarring as other examples though, as it's all played for laughs.
This is the signature style of Andrei Belyanin, whose novels are deliberately filled with anachronisms. Justified in several cases due to magical settings and/or Time Travel. Since his books tend to be humorous in nature, the readers don't mind it in the least. The attempts of a modern-day cop at lecturing a medieval tsar on the concept of "innocent until presumed guilty" (instead of the tsar's usual Off with His Head! approach to all suspects) and the need for a proper investigation are downright hilarious. Sometimes, though, it makes no sense, such as in Jack the Mad King, where Jack is talking with a giant using modern-day street slang.
This is generally averted for historical settings in Time Scout, as the authors attempted to be as accurate as possible. However, the time terminal that forms the main setting is deliberately a stew, and justified, as every time gate is surrounded by a lot of shops and restaurants based on that time period's theme, and the time terminal's residents wear whatever they want and tend to wander. Connie Logan, proprietor of Clothes and Stuff, is walkingAnachronism Stew, wearing multiple articles of clothing from multiple periods as she tries out new designs for comfort and wear. She switches out multiple items over the course of a conversation. As for the historical destinations, the authors tried, but made a few mistakes. Not egregious.
Invoked in Return to the Willows, a fan-written followup to The Wind in the Willows, when the characters must dress in armor to disguise themselves, but in order to get everything to fit have to mix 17th and 18th century armor, which one of the characters notes normally shouldn't be done.
The children's book Koziolek Matolek. Matołek encounters brigands straight out of a fairy tale, visits a medieval castle, ends up in feudal China, later travels by plane to Poland and drives a car...
The Mummy or Ramses the Damned by Anne Rice. It's set fifty years after Verdi wrote Aida, which makes it The Roaring Twenties, but the fashions are Victorian, no-one mentions the First World War, and the Egyptian Department of Antiquities (founded 1858 to ensure that Egypt got first claim on their own treasures) doesn't appear to exist.