Possession is the supernatural ability for a spirit to take over a physical body. The act usually results in the total subsumption of the host's mind and will but not always. Only two known species have been known to possess with the rare occasion of another species that is not normally capable of it.
Kitsune
Spiritual Kitsune such as the Nogistune is capable of possessing a host, most of the time it completely takes over its host but one instance had a yakuza member who seemingly allowed himself to be possessed to climb the ranks, its not known if he had conscious control or not.
Hellhound
Hellhounds whether there is only one or not, are capable of possessing a host, unlike the Nogitsune, the Hellhound's method is more benevolent, allowing its host to live its life in a normal manner until the spirit within has a duty to fulfil. The host, even when in control, benefits from some of the abilities of the hellhound, such as super strength and fire immunity.
Hellhounds can fully merge with their host, allowing them to become more powerful as they are then in sync.
Werewolf
Werewolves can't really possess but Peter Hale was able to imprint himself onto lydia, and was able to subtlely control her actions through dreams and hallucinations.
Sebastien Valet's spirit was somehow summoned by the Dread Doctors and successfully possessed Mason Hewitt, essentially becoming resurrected. Sebastien was also able to access Mason's memories which allowed him to learn how to drive.