No Mythical Pokémon is allowed in ranked battles, or in any battle facility with a banlist. As for legendaries, Articuno, Zapdos, Moltres, Raikou, Entei, Suicune, Regirock, Regice, Registeel, Latias, Latios, Uxie, Mesprit, Azelf, Heatran, Regigigas, Cobalion, Terrakion, Virizion, Tornadus, Thundurus, Landorus, Type: Null, Silvally, Tapu Koko, Tapu Lele, Tapu Bulu, Tapu Fini, Kubfu, and Urshifu (and most likely Regieleki, Regidrago, and Calyrex when the Crown Tundra is released) are allowed in ranked battles and battle facilities in all generations they appear in (along with the Ultra Beasts, which aren't officially considered legendaries but are internally classified as such in the game's code). Additionally, several battle facilities allow any Pokémon including those banned from other facilities, including the Lv. 70+ modes of the Battle Tower in Crystal, Trainer Tower in FRLG, Trainer Hill in Emerald, and the normal non-Super modes of the Battle Tree in USUM.
