Mythical Pokémon

Mythical Pokémon were originally known in common conversation as "Event Only Pokémon" for a reason. These Pokémon are so rare that they are typically only available through going to an event distribution and either receiving the Pokémon itself, or an item to go get the Pokémon within the wild. Due to the fact that these are typically only from events and have limited distributions, these Pokémon are banned from Battle Tree, Battle Frontier and similar facilities, as well as the Rating Battles in Battle Spot & the Video Game Championships . Several instances of Online Competitions have allowed for the use of these Pokémon. They have typically have base stats that sit around 600, and some even have Form Changes or Mega Evolutions causing stat increases.
The Generation 7 Pokémon games also introduced the first evolving Mythical Pokémon

Mythical Pokémon
Mew
Synchronize
Celebi
Natural Cure
Jirachi
Serene Grace
Deoxys
Pressure
Phione
Hydration
Manaphy
Hydration
Darkrai
Bad Dreams
Shaymin
Natural Cure
Arceus
Multitype
Victini
Victory Star
Keldeo
Justified
Meloetta
Serene Grace
Genesect
Download
Diancie
Clear Body
Hoopa
Magician
Volcanion
Water Absorb
Magearna
Soul-Heart
Marshadow
Technician
Zeraora
Volt Absorb
Meltan
Magnet Pull
Melmetal
Iron Fist
Zarude
Leaf Guard
Pecharunt
Poison Puppeteer