Let's begin at the beginning: Dungeons & Dragons(and most other Medieval European Fantasy settings for that matter) normally does not have firearms, yet you can usually get your hands on a rapier, a type of sword that wasn't developed until(and because of) the proliferation of early guns.
Space 1889 well, it is Victorians in Space meeting canal Martians which have a pre-industrial society with some leftover technology from a much more advanced era, stone-age Hill Martians and High Martians on Mars and stone-age lizardmen and dinosaurs on Venus.
King Arthur Pendragon takes a mix of all the main Arthurian myths, mostly Malory, and sets it in sub-Roman Britain. The appearance of medieval technology later in Arthur's reign is explained by magic and it all fades away after the Battle of Camlann with history re-asserting itself.
Pendragon is not above shout outs to later history either, including Merlin prophesying that the Pope would live in Avignon, and King Arthur quoting John F. Kennedy "ask not what your country can do for you..." before the Battle of Badon Hill.
Parodied in the Tabletop GamesDiana: Warrior Princess and Elvis: The Legendary Tours, which take the Anachronism Stew approach to modern-day pop-culture.
Quirkily lampshaded by the SourcebookGURPS Middle Ages. Its opening chapter includes a sidebar that actually explains the concept of Anachronism Stew by pointing out all the historical mismatches in its own cover art.
Also acknowledged in GURPS Camelot, the Arthurian sourcebook. There are three Arthurian settings mentioned - the Mythic one (Geoffry of Monmouth style, with plenty of anachronism), a Realistic one (as close as research can get us), and the Cinematic one (based on movies, with chrome armor and French castles and all the other goodies - not so much Anachronism Stew as an Anachronism Smoothie).
Mythic Russia has a few that are pointed out and justified in the book. The Russians drink vodka even though it hadn't yet become popular historically, because "what is a game in Russia without vodka?" The Mongols are Tengrist pagans even though the Golden Horde had converted to Islam by the time it was set, partly because it's easier to handle in the game's Religion Is Magic system and partly because of plain old Rule of Cool.
The Pirates Constructible Strategy Game by Wizkids is a naval combat game set sometime before, during, and after the American Revolution/War of 1812 era. When the first set came out, things were fine, but with each new expansion, they seem to be intent on adding a new crazy mechanic. They get alright justifications/Handwaves most of the time, but it is still silly. They are currently halfway between this and Fantasy Kitchen Sink. Some of these include:
Bombardiers (Ships with long-range and flame cannons attached to their decks)
Turtle ships (which at least existed around the time)
"Switchblades" (metal ships with giant pincers attached to the sides)
The old Atlantean Trilogy by Bar Games mixed Anachronism Stew with All Myths Are True, and came up with an alternate Earth where Atlantis coexists with Avalon, Amazons rub shoulders with gypsies, and you can sail from Hyperborea to Nazca. Never mind it's supposed to be set in 15,000 BC, and the continents' geographies are radically different?
The defunct trading card game Anachronism was built on this trope. The idea was that you could play as, say, Ivan the Terrible while wielding a claymore, wearing Japanese armor, and with Aphrodite on your side.
The Yu-Gi-Oh! OCG name for the Chronomaly archetype, "OOPArts", is an acronym for "Out-of-Place Artifact", a term used to describe artifacts that make no logical sense given the technology available at the time they were created. The TCG name, "Chronomaly", is a portmanteau of the word "chronology" which is the sequential order in which past events occur and "anomaly" as in an irregularity or something odd. Put together these monsters are "chronological anomalies" or "chronomalies" since these objects deviate from what would have been possible to create given the resources and technology available at that time.
Note that this isn't even the most notable example. From the very start, there were magicians, knights, dragons, and the like along side stuff like tanks, military infantry, and both ridiculously human and Super Robots.
The one most people have pointed out in Fantasy Battles is Bretonnia, which is an Arthurian-style Fuedal Kingdom with your traditional knights, bows, and trebuchets, right next door to the Empire, which is nearly 2-3 centuries ahead with cannons, guns, and tanks.
Other examples in the game (there are many) include the Skaven, who have access to Gatling- oh wait - Ratling guns and Lightning cannons, while other races, such as the Elves or the Tomb Kings, still use ballistae, bows and chariots.
Warhammer40000 has this as well, with many troops (especially Orks) being armed with bladed melee weapons such as swords, axes, and warhammers, while others have machine guns, lasers, automatic bazookas, and space ships.
Characterized even farther by the fact that the lore states there are planets that have slid back technologically to a Medieval Stasis from being cut-off from other worlds, which may have been used at one point in early source books to try and incorporate the Warhammer Fantasy Battle universe into that of 40k.
Hoyle's Rules of Dragon Poker: The author never bothers to explain why a game played at ancient Pompeii has rules for surge protectors and Weird Al.