Mythology
In the old days, before science existed, people sought explanations for why the world existed as it did. Humans being humans, their first explanations revolved around ascribing humanlike characteristics to natural phenomena, which in turn became the first gods worshipped by humankind.
From there, stories spread about the nature of the gods, as well as other stories that sought to explain such things as the origins of humankind, what happens after death, or the exploits of ancient heroes. Many other mythical creatures are thought to have started the same way- for example, stories of giants being inspired from the fossilized bones of mammoths. As these stories passed down from generation to generation as either legends or religion, it gave birth to the fantasy genre we all knew and love.
In a sense, mythology is a blend of history and fantasy, with elements of what might have really happened wrapped up in cultural beliefs and shaped by the worldview of its originating society. Even in the present day, more than a few such myths are still prevalent despite their no longer being openly supernatural (e.g. George Washington and the cherry tree).
Older myths often contain bizarre and fucked up shit like incest and rape because people in ye olden times were fucking deranged and kinky as all hell, and as far as they were concerned, nothing was off limits. Of course with different cultures from country to country, mythology can be quite different and they all had their own angels and demons/spirits/energies based on how their own cultures perceive them.
Connection with Fantasy Genre
As you can see, many an author took interest at the old legend and decided to include its elements in their own stories. Notably, Tolkien took many elements from the Norse and Germanic Mythologies and popularized the concept of fantasy races like Dwarfs and Elves.
Mythologies
Greco-Roman
There's a god for every aspect of ordinary life, like smithing, governing and war. The most important gods/goddess you need to know are Jupiter/Zeus, the guy with the lightning power who is the god of all gods; Minerva/Athena, goddess of wisdom and war born from Jupiter having a massive headache fully grown up and armed; Dis Pater/Hades, Jupiter's eldest brother and the god of most of the Greco-Roman afterlife; Neptune/Poseidon, Jupiter's other brother and the god of the seas.
According to Greek myth, Uranus (the first kinda ruler of the Universe) was killed by his children, a race of giants known as the Titans. Cronus, the last born of those giants and the one who took up Uranus' throne, fears that he might be killed by his sons one day just like his father so he ate each one of them as a new one is born from his wife Rhea, but Rhea hid Zeus and fooled Cronus into eating a rock. Zeus then grows up and kills his father, saving all his brothers and sisters inside his father's belly (and who were somehow undigested), thus igniting a war that leads to the overthrow of the Titans. This event is known as The Titanomachy (Battle of the Titans). After all the Titans had been slain (or imprisoned in the Underworld, which amounts to the same thing), Zeus formed a government with the rest of his gods while living a comfy hedonist life where he raped many mortal girls and had many bastard sons for the lulz.
Roman myth can't agree on anything, because, unlike Greacian legends, it isn't racist and isolationist as fuck and takes from all Indo-European religions it encountered. This also means that it deviates from the "twelve important gods" rule that the Greeks had, and every area and time period had its own important gods. Imagine it as something akin to ancient Hinduism, minus all the mysticism (at least until all the Egyptianesque mystery cults started popping up at the dawn of the Empire).
Most notable heroes with lots of media adaptions: Hercules, Daedalus, the leaders of both sides of the Trojan War (Achilles, Hector, Paris ect.).
Most notable villains in media adaptions: Zeus (as a giant dick of a King), Hades (only a villain in media adaptions; the original Hades was considered highly honorable), the Titans and their spawn, Ares.
Interestingly, Eldar and Elves of the Warhammer worlds took a lot of elements from Indo-European myth, the prime examples of the west being Greco-Roman mythology.
Norse
Like the Greeks, there's a god for every aspect and their most hated enemies are tower tall humanoid creature who the gods/goddess also related to, but were called Frost Giants instead of Titans. The Norse mythos contains a lot more references to snow, winter and wolves than the Greek one. This is somewhat unsurprising.
Basically, in the early world's life cycle, there were these Frost Giants who were sweats born from the armpit of Ymir, the first of giants. There was also a giant cow, Audhumla, the udder of which Ymir frequented. Then that giant cow accidentally created a god by just licking a salty rock, Buri, who then "begat a son" - fuck knows how. This son, Bor, had a wife Bestla who gave birth to Odin and his brothers. Odin does not like giants since they come out of Ymir's stinking armpits like rats and they eat a lot so he and his brothers Vili and Ve killed Ymir. Ymir was so fuckhuge that his blood caused a massive flood that killed other Frost Giants. Odin then used Ymir's body to forge a new world. The death of Ymir also brought forth many life forms without Odin's touch like the Dwarves, who were basically Ymir's corpse maggots. Then like the Greek gods, Odin formed a government with gods/goddess of each daily life aspect. And then Ragnorok will come.
Most notable heroes with lots of media adaptions: Thor, Sigfried/Sigurd.
Most notable villains in media adaptions: Loki, Fafnir.
Dwarf
While there many mythologies that have different telling of the dwarf race, we will be talking about the norse version.
After Odin murderfucked Ymir and killed a bunch of giants through blood flooding (see above) maggots came out and were festering on Ymir's flesh. Yes. These corpse maggots are the will be precursor of the dwarfs. So god found these maggots and turned them into the dwarf we all knew and love. They have the talent of mead brewing, metal smithing and making magical artifact. Many of iconic weapon like Thor's hammer are crafted by the dwarfs. But most importantly of the dwarfs creation is perhaps Odin's spear, why? BECAUSE IT IS NAMED "GUNGNIR"!! that's like the name of the warhammer dwarf god "Grungni", only with the letter "r" in the wrong place.
Anyway, other things about dwarfs is that they can turned to stone if they exposed to the sun for too long (wtf were they vampires too?). They are sometimes refer to as "black elf" since they were corpse maggot and they were described as being dead or resembling human corpses.
There are also four known dwarfs in the mythologies: Austri, Vestri, Norðri, and Suðri (which means “East,” “West,” “North,” and “South”) and they got the crappy job of holding the corner of the sky (aka the Atlas treatment) just because they have super strength.
Elves
In Norse myth, they were demi-god like beings whose sole purpose is to be more beautiful and superior-than-you. They are described as "more beautiful than the sun" with their demi-god status apparently linked to the gods of Vanir and Aesir. Their lord is a Vanir god called Freyr, who rules the elves’ homeland, Alfheim. They commonly cause humans to suffer illness but have the power to cure any illness only if sacrifices are offered to them, what a bunch of dicks. It is also possible for humans to become elves upon death. Elf and human can also interbreed; the mix of human and elf is described as having the look of a human but possess extraordinary intuitive and magical powers.
Christian
The one everyone most familiar with in the western countries since you can learn them in church.
Much of the Christian mythology is drawn from the old Hebrew bible though has been expanded considerably by Prose and Poetry over the centuries meaning that there is a wealth of third-party, non-canon material out there for DMs to use in their campaign settings. Christian mythology is one of the many mythologies that were derived from Jewish mythology, the same goes for Islamic mythology and many others from Middle Eastern countries.
So in Christian mythology there's only one god: YHVH, which most people would just refer to him as THE GOD since his name is too sacred to spoke of. In fact, we don't even know how its pronounced, the two most common anglicizations being Yahweh and Jehovah.
Before the world was born, according to Milton - there was this "war of heaven" (not this one) where Lucifer, the most perfect of the god's creation, the best of the archangels rebelled against God with some other angels, but was defeated and cast down to hell where - according to Dante (not this one) - there are nine levels of Hell (not these ones) and Lucifer is trapped in the lowest leyer, stuck inside a frozen lake of his own tears. Lucifer also has three faces, whose face is similar to the sinner he chewed on: Judas (betrayed jesus), Brutus, and Cassius (betrayed Caesar).
After that, god creates the world. It is said that the god created the world in 7 days, hence the Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday. He then created many animals, plants and the two human: Adam and Eve. He observed them in the Garden of Eden (aka his research facility) watching them having fun and telling them that they could do anything they wanted, except from eat the fruit of one particular tree in the garden. But that promise was broken when the girl, Eve was tempted by a winged serpent -who according to Milton, was actually Lucifer in disguise - to eat the fruit. Adam and Eve having eaten the fruit, gained knowledge and dignity which made them embarrassed by their lack of clothing. God found out and exiled from the garden them to the mortal world. The serpent is also punished with his wings taken from him, turning him into the snek we all knew and feared.
In the mortal world, Adam and Eve worked hard to survive and later conceived two sons: Cain and Abel. Cain was a farmer while Abel was a butcher. When they both offer their produce to God, God only favored Abel's (according to some, it was because Cain hid his best offering from god. By this point if you are a true Vampire: The Masquerade fan, you would know what's coming next, but without the vampire shit.) Cain's punishment for murder is to never farm ever again; wherever he spilled his brother's blood, the earth became cursed so that it can never grow anything. Basically denying Cain's favorite job and career. However, punishments differ in other mythologies and it's a clusterfuck. Adam and Eve later had the third son Seth, which is the true ancestor of mankind and Cain is then exiled to the land of the Nod where he built the City of Enoch (because he can't farm) and conceived many other decendents. There's also the claim that Eve was not the first wife, but Lilith, a woman who was created from the same dirt as Adam. Felt too hot shit for Adam, so she ran away with an archangel called Samael (the Fallen name for Lucifer in some stories) though in other stories she ran away a demon prince called Asmodeus (not probably this one) and begat a whole race of demons called the Lilim or Lilitu. In Vampire: The Masquerade however, she taught Cain cool dark magic and shit.
Most notable heroes with lots of media adaptions: Jesus, Samson, David, Moses, Noah.
Most notable villains with lots of media adaptions: Satan/Lucifer/The Devil (may or may not be the same character), Judas Iscariot, Cain (the first murderer).
Noah's Ark
There was also this apocalyptic event where god being a dick or his computer hard drive malfunctioned so it causes the sea level to suddenly rise to the kind you see in disaster movie like The Day After Tomorrow. He instructed a guy named Noah to build an ark big enough to contain every animals and humans in the world, or just each animal species with their own female and male pairing so that they could reproduce. God even instruct Noah to build the ark with the size he demands: 300 cubits in length, 50 cubits in width and 30 cubits in height (450 × 75 × 45 ft or 137 × 22.9 × 13.7 m), it's almost as if god intended this. The ark is also made out of some probably extinct wood called "Gohper", probably the best kind since the ark has to withstand waves after waves of tsunami for a long time and a tragically, all of them are probably used up just for the ship. After the flood came and everyone is on the ark, they basically float for about 150 days until the water goes down.
Moses and the Exodus of the Hebrew
Another myth took place in Egypt. There once lives the Hebrew (Jewish) people, the gods chosen (yeah, they are arrogant like that). They were living in peacefully harmony until one day some asshole Pharaoh came and starts to oppress the shit out of them. The Pharaoh hates how the Hebrew breeds like rat so they had every one of their male children to drown in the river of Nile. Moses, our hero of the story survived as an infant and was adopted by Pharaoh's daughter (oh the irony). Moses eventually grow up and learn of god's name Yahweh and tells him to free his people and guide them on an exodus to the promised land. Pharaoh and his army tried to stop them but god basically said fuck you and send ten powerful plague to fucked them over. The plague is so effective that Egypt became a frigging wasteland, but no undead unfortunately. Later, Moses guide his people to close the red sea where he do the iconic sea splitting to make a crossing passage. The Pharaoh and his goons tried to take chase but was once again pwned by the sudden sea crushing them both side when they were on the sea passage(god really hate Egyptian huh?). After traveling with his fellow Heberew, Moses decided to talk to the god on the mountain for sometime and came back with the Ten Commandments, ten rules willed by god and if these rules were crossed, the severity of the punishment will be depend on which rule was broke (Ex. commit heresy like worshiping other gods will be awarded with genocide of the entire cities of man, woman, chidren and animals). Unfortunately, some of his unfaithful followers were slacking off and was worshiping some chaos-looking-brother-fucking-golden-bull-idol and was ordered by Moses to have them execute. Moses and his follower eventually arrived to their promised land, which is, unsurprisingly, modern day Israel! which the Hebrew will remain and fight over with their unfriendly Islamic neighbors for the next eternity or so.
Things drawn from Abrahamic Myth / Demonology
The "bibles" (Jewish, Christian and Islamic holy books) and associated apocrypha are undoubtedly HUGE sources of inspiration for game developers, particularly Dungeons and Dragons where monsters are ported over, virtually unchanged and names of significant figures are also often used.
- The idea that Hell has Nine layers - Baator - though where Dante's layers have distinct punishments, Baator's layers are the realms of powerful lords.
- Names of significant demon/devil characters: Asmodeus - demon of Lust, Baalzebul (or other variants like Baalzebul, Beelzebub) - demon of gluttony, or Mammon - demon of avarice
- Different orders of Angels, or angel analogues such as Genies
Egyptian Mythology
Most well known for its collection of gods with the heads of animals. Unlike Greek or Norse mythology, has very little emphasis on mortal or demimortal heroes.
Egyptian mythology is wildly inconsistent due to spanning numerous cultures over thousands of years: for instance, the world is alternately said to have been created by Ra, Atem, Ptah, Thoth, or a collection of eight gods known as the Ogdoad. Whoever was the supreme god mainly depended on what city you're in and what time period it was, but the most well-known one was the sun god Ra. A common theme was the maintaining of a divine order known as Ma'at. Maintaining Ma'at on Earth was seen as the prime responsibility of the Pharoah, a priest-king who was seen as the bridge between mortals and gods. Another major theme is the concept of the death and rebirth of mortals and gods alike, leading to the famous Egyptian practises of mummification and the construction of elaborate tombs.
Most notable heroes with lots of media adaptions: Anubis.
Most notable villains in media adaptions: Seth.
Japanese Mythology
Japanese laymen don't really bother separating their major religions, and thus the major religions (Shinto, Buddhism), some more minor ones, and various folk heroes exist simultaneously. Rarely touched by non-Japanese works that aren't the pantheon for Japan analogs.
Most notable heroes with lots of media adaptions: Susano-o (Anti-Hero), the Buddhas.
Historical people ascribed mystical powers Himiko, Abe no Seimei, Masakado, Tomoe Gozen, various Sengoku leaders especially Hattori Hanzo and self-proclaimed demon lord Oda Nobunaga.
Most notable villains in media adaptions: The Orochi, oni, various Buddhist demons and evil types of yokai.
Artifacts: The Imperial regalia (Kusanagi, Magatama and the Yata no Kagami) and various katana made by famous people.
Arthurian Mythology
The story of a boy who becomes a king and his knights. Arthurian lore is unusual among mythology in that historians actually know the names and history of the authors who created most of it. This doesn't make it any more consistent and in-fact even authors directly continuing existing stories couldn't be assed to keep basic things consistent.
Most notable heroes with lots of media adaptions: Arthur, the Knights of the Round Table, Merlin.
Most notable villains in media adaptions: Morgan le Fey, Mordred, the Green Knight, the Black Knight. Arthur's original nemesis of the Roman Empire virtually never shows up in adaptations.
Artifacts: Arthurian myth has some of the highest artifact density out there. Among the most famous are the grail, the sword in the stone, Excalibur, the green girdle and occasionally the round table itself.