I don't know about published settings but in my setting a wide variety of evil creatures and Beings can possibly possess others under the right conditions, even by force.
And a wide variety of good creatures and Beings (Angels, Ki-Rin, etc) can also possess others if the one to be possessed agrees voluntarily to do so, and the possession has agreed upon limits, like an objective (to achieve a certain end) or has a limited timeframe.
Good possessions are usually more in the way of guiding the character and/or allowing the character to amplify and augment or maximize their own natural abilities and capabilities and is called "Enthusiasm" which literally means "god within - theos en." Sometimes though the good possessor will allow their abilities (within reason and restriction) to be used by the one being possessed and that is called "Parisma" (parallel Charisma).
Evil possession is called simply Possession (though there is more than one form of it) and is usually done by evil creatures not to give the characters special abilities but to use and/or endanger the player character for the ends of the possessor. Although familiars and demons can possess certain NPCs or others at will by prearranged contract or agreement.
I have no character races that naturally possess others as an ability, but plenty of both good and evil NPCs who have done it on occasion. But now that you mention it certain types of possession would make great high level evil Cleric, Sorcerer, and Warlock spells and capabilities, and Enthusiasm and Parisma would make great capabilities or miracles for high level good Clerics.
