Possessions (also known as Psychokinetic Biological Inhabitation) are where the spirit invades the body of a person or an object, causing them to work to a degree under the spirit's influences. This event has happened all throughout the Ghostbusters Franchise.
In the first movie both Dana Barrett and Louis Tully were possessed by Zuul and Vinz Clortho respectively. They subsequently acted irregular in behavior and were instrumental in bringing Gozer into the world, transforming into Terror Dogs in the process.
Ghostbusters: The Video Game
In Ghostbusters: The Video Game, many ghosts have the ability to influence or possess people and objects. The notable examples are the Golems, entities created by ghosts infusing various objects into one. There are Possessor Ghosts that could possess people and statues. Also, Ivo Shandor's spirit possesses the mayor Jock Mulligan. To Read more on Possession in Ghostbusters: The Video Game, go here.
Secondary Canon History
The Real Ghostbusters
Many creatures in the series have the ability to possess people or objects. One notable example is Wat, who temporarily possessed Peter Venkman. Also, ghosts such as the Grundel are able to partially possess humans.
The new team battled some possessors, like the Ghostmakers and Gu Mo. Also, Luco and Ravana were able to partially possess humans. Vampire Clowns were able to "possess" people with their power and transform them into their kind.