Baba Yaga is the most infamous figure of Russian folklore and mythology, hands down, being the only character anyone who isn't Russian can probably name. A hag's hag, Baba Yaga varies wildly between different stories from standard child-eating ungodly abomination to a chaotic trickster mentor, who can be both ally and enemy depending on her mood and how much respect you show her. Some of the few things that remain constant; she flies in a mortar and pestle, she has a sweet-ass house that moves by walking along on giant chicken legs, and you do not fuck with Baba Yaga.
Dungeons & Dragons
Since Dungeons & Dragons has always been a melting pot of influences, it goes without saying that Baba Yaga has made her appearances there. In fact, her famous Dancing Hut appeared as a potential artifact in 1976's Supplement III: Eldritch Wizardry, before being updated in the Advanced Dungeons & Dragons Dungeon Master's Guide of 1979 and the Book of Artifacts in 1993.
But what about the old witch herself? Well, Baba Yaga first appeared in the Dragon Magazine article "The Bogatyrs of Old Kiev," in Dragon #53 in 1981. Here, she was a powerhouse, with a combined level and multiclassed power set that many gods would envy: Fighter 12/Druid 10/Magic User20/Illusionist 15 - in 5e mechanics, that adds up to a freaking level 57 witch!
If that wasn't impressive enough for you, Dragon #83 in 1984 featured the adventure "The Dancing Hut", with a version of Baba Yaga that was even more powerful than before, as well as converting her Dancing Hut from a mere artifact to a demiplane tesseract. This was then followed by the adventure module S5: The Dancing Hut of Baba Yaga, in which the party were trying to prevent the old witch from capturing the power of Death itself, thus eliciting the attention of the forces of Light, Darkness, and Twilight.
There was an AD&D Gamebook called "Nightmare Realm of Baba Yaga" which, as you might surmise, featured her prominently.
Baba Yaga came to the fore in Dungeons & Dragons 4th Edition. In the World Axis cosmology, Baba Yaga is an Archfey, whose most common title is "Mother of Witches"; first mentioned in the 4e Manual of the Planes, she made a triumphant return in Dungeon Magazine #196, where she had both her own Court of Stars article and a new iteration of the classic "enter Baba Yaga's dancing hut" adventure.
Baba Yaga has also made her influence on the D&D canon felt in subtler ways; for example, the infamous witch of Greyhawk, Iggwilv, is rumored to be one of Baba Yaga's daughters, whilst she was instrumental in creating the Demon Prince Kostchtchie and, although she doesn't appear in the module, the character of Baba Lysaga from 5th edition's Curse of Strahd is clearly based on her, complete with the walking house.
However, it is in Pathfinder that she has truly shone, as Paizo has no shame about stealing from real-world myth and folklore to pad out Golarion. Baba Yaga is a central figure of the Reign of Winter Adventure Path, which lays her entire history and power set bare in its final issue. Born on Earth in 75 BC, she managed to become a powerful witch despite coming from humble antiquity Sarmatian peasant girl stock when she was taught the arts of sorcery by a powerful faerie for shits 'n' giggles. As her powers grew over the centuries she became renowned in regional Slavic folktales. She would eventually begin to travel the planes and, about 1,500 years ago, she made a few visits to Golarion before deciding it would be a nice place to put down roots. With an army of ice trolls, giant wolves, frost giants, white dragons and other evil creatures of cold and fey nature, she overran the eastern half of the Ulfen kingdoms. After winning this Winter War in less than a month she carved the new territory into her kingdom of Irrisen, locked the entire country in a perpetual winter, put her eldest daughter Jadwiga on the throne, and then promptly fucked off, a process which repeats every one hundred years. When she returns she collects her daughter and all her children, and installs another one on the throne to rule for another century, and then fucks off again. The only thing scarier than what Baba Yaga does to her daughters once their rule is at an end is what it is like to actually have to fuck Baba Yaga for her to get those daughters in the first place. Occasionally one of Baba Yaga's daughters will attempt to resist being dethroned, knowing that whatever fate awaits them can only be grim, but it generally ends poorly and swiftly for them as Baba Yaga is as wily as she is powerful.
Baba Yaga's lore is actually written to imply, without stating it for legal reasons, that this is the same Baba Yaga used in D&D. The author for Rasputin Must Die took this to the ultimate conclusion. In a forum post he gives an unofficial conversion that details how, if your group wasn't of the temperament to enjoy traveling to World War I Russia and fighting Rasputin in a reverse Isekai, you can instead have it be about going to Oerth and fighting Iuz. Since both Rasputin and Iuz are descendants of Baba Yaga, and both Russia and the Empire of Iuz are close enough in weather (lots of snow) this change requires surprisingly little modification.
Vampire: The Masquerade
In Vampire: The Masquerade, Baba Yaga, also known as Medusa, yet another alias of hers, is one of the many names of the Matriarch, progenitor of the Nosferatu.
The Matriarch, a figure shrouded in mystery, is a horrendously powerful Nosferatu Methuselah in White Wolf's World of Darkness. Once a beatiful young woman and a shaman of her tribe, she defied Absimilard, a Antediluvian, who is one of the greatest sick fucks in World of Darkness. She did this as a mere mortal, making her the Ollanius Pius of VtM. Pius died in glory however, but the Matriarch?
She was brutally raped by Absimilard, turned into a vampire, and became one of his concubines. After Caine cursed Absimilard to be uglier than the shit I took yesterday, the curse also went to his childer, making them look like atrocious monsters. After the fall of Second City, she managed to break her blood bond, the mystical chain that made her a slave to Absimilard, with no help from anyone, showing that her willpower stat is over 9000.
In spite, she sired the Nosferatu clan and went to war with Absimiliard. Absimilard sought to kill all his descendants, due to being scared shitless of Caine, who commanded the Antediluvians to keep their generation and numbers low, unless they wanted another "visit" from him, meanwhile the Matriarch was siring childer every fucking night while wandering the world. Anyway, she either drove Absimiliard to torpor in Antartica, or sent him fleeing to the depths of the Atlantic Ocean. It's unknown how she managed such a feat, but it happened most likely thanks to the help of Koshchei the Deathless, a Talon of the Wyrm. After that, she took the name Baba Yaga, and claimed the lands of Russia as her domain. She fell into torpor a few centuries later, only waking up during Cold War, when she created the magical Iron Curtain that caused the rest of the supernatural world to be cut off from Soviet Russia during the while she did bad things to those pansy Brujah commies inside. A charming specimen, she was an eight foot tall vampire with iron claws, iron fangs, skin covered in pustules, and a stereotypical long crooked nose. She was later killed by another childe of her sire, a Nictuku (scary Nosferatu-hunting vampire assassin) that took the form of a small girl by the name of Vasilisa. If this sounds like a certain Russian fairy tale, you're paying attention.
She was certainly evil, but held the line against a even more terrible evil, her sire, one of the Antediluvians. That certainly deserves respect.