The best thing about being in the public's eye is the questions you get from students of Hellenismos. Even if it's something I have no experience with or knowledge about, it's very interesting to puzzle together answers. Take this one; Martin from Puerto Rico sent me an e-mail concerning exorcisms. He writes (in part):

"[A] friend of mine was talking about exorcism and knowing I follow the Greek religion he ask me if we had something like Christian exorcism. Is there?"

Exorcisms have a long and varied history, and the best known version of it is the 'Major Exorcism' as performed by a Catholic priest. This rite is recorded in the Rituale Romanum which seems to date from around 1600 AD. How old the ritual itself is, I am not sure, but the concept of possession is most certainly ancient. The idea of the Major Exorcism is to establish that a demon has taken possession of a person--which should be measurable by certain signs like speaking in tongues and convulsing--and then to drive out the possessor by reciting ritual texts and presenting the creature with holy iconography.

The question makes a few assumptions that need to be addressed before answering your question:
  1. Did the ancient Hellenes believe in possession?
  2. Did they believe it was a bad thing?
  3. Did the ancient Hellenes believe creatures which classically possess humans and/or animals existed?
  4. Did they believe these creatures would, indeed, possess humans and/or animals?
  5. Was it possible to cast out these creatures through religious (or even secular) rites?
The short answer to the first question is yes, they did. Certain Gods--especially wilder Gods like Dionysos and Pan were said to influence their followers in such a way that they became unaware of their surroundings and actions. The Maenads--followers of Dionysos, often female--in mythology at least are often portrayed as tearing people apart in their fit of madness and to see things while doing so. Most often, this is the way they are tricked into committing these acts. Almost always, they are inspired to do so by Dionysos Himself. The longer answer is a debate on if this constitutes possession as laid out by the Roman Catholic church. In the Rituale Romanum, the signs of possession are described as follows:

"[The] ability to speak with some facility in a strange tongue or to understand it when spoken by another; the faculty of divulging future and hidden events; display of powers which are beyond the subject's age and natural condition; and various other indications which, when taken together as a whole, build up the evidence."

As you can see, it leave a lot of room for interpretation. While the actions of the Maenads might fit part of the bill, it is more interesting to look at oracles as subjects of possession, as they tended to speak in tongues or riddles, divulge hidden events, and would often show physical signs of not being in control of their bodies. The oracle at Delphi is a classic example, and indeed, the ancient Hellenes believed the oracle possessed--not by an evil entity, but by a God; in this case, Apollon (for the majority of history anyway).

As such, I don't believe possession in these forms was considered a bad thing; it was the way the Theoi spoke to or through their followers, and in general, it was a much sought-out and desired skill of both mystery cults and divination.

Classical creatures who possess people according to the church are mostly demons, malevolent beings sent by the Devil or acting on their own accord. In general, their only goal is to bring pain and suffering to humanity. The word 'demon' comes from the ancient Greek root 'δαίμων'--'daímōn'. Hesiod gives us our first glimpse into daímōns as he writes about the five Ages of Man in 'Works and Days'. He gives us the following references:

"First of all the deathless gods who dwell on Olympus made a golden race of mortal men who lived in the time of Kronos when he was reigning in heaven. [...] But after earth had covered this generation -- they are called pure spirits dwelling on the earth, and are kindly, delivering from harm, and guardians of mortal men; for they roam everywhere over the earth, clothed in mist and keep watch on judgments and cruel deeds, givers of wealth; for this royal right also they received.

[...] then they who dwell on Olympus made a second generation which was of silver and less noble by far. It was like the golden race neither in body nor in spirit. [...] But when earth had covered this generation also -- they are called blessed spirits of the underworld by men, and, though they are of second order, yet honour attends them also." [ll. 109-120]

Hesiod's Ages speak of only one race who became daímōns; those of the Golden Age, yet those of the Silver and Heroic Age also received many honors after their passing, and they were held in high regard. Hesiod makes clear distinction between the Theoi and daímōns: the Theoi are Gods, daímōns are members of the Gold Age who gained immortality. This differentiation is much less pronounced in the writings of Hómēros, where God and daímōn are used virtually interchangeably.

This difference led to a misinterpretation of the nature of the race of the Silver Age: they became dangerous daímōns in the eyes of later writers (like Plato), and eventually the demons of Christianity. Yet, neither Hómēros or Hesiod ever intended them to be so: all daímōns were pure and Deathless; they acted as a policing force for humanity. Especially through Neo-Platonics comes the placement of daímōns between the Theoi and mankind. They are less powerful than the Theoi, with lesser domains; more concerned with the daily happenings of life than the Theoi are, but they, too, are immortal, and deserve honors. Daímōns fulfill an important role in mythology and life: all aspects of life can be overseen by Deathless beings, without taking away from--or needlessly adding to--the portfolio of the Gods.

A daímōn could also be a personal guardian spirit or the personification of a person's conscious--or even their muse--this idea seems to be a Neo-Platonic evolution of Hesiod's classical daímōns, popularized by Socrates (and his followers), who described his personal daímōn in his trial. From Plato's 'Apology':
"You have often heard me speak of an oracle or sign which comes to me, and is the divinity which Meletus ridicules in the indictment. This sign I have had ever since I was a child. The sign is a voice which comes to me and always forbids me to do something which I am going to do, but never commands me to do anything, and this is what stands in the way of my being a politician."

Daímōns had been separated from their Hesiodic cousins by then, but they were still considered positive forces. The later corruption of the term came from the Christians. The ancient Hellenes did not know demons in the way we know them now; the earliest mention I know of is from the Papyri Graecae Magicae, which also includes an exorcism rite. Note that this document can be dated anywhere from the 2nd century BC to the 5th century AD, and that it was Graeco-Roman/Egyptian in origin. It was a rather obscure document even in its time, but for this search, it might suffice. Note that it is in essence a Christian rite, though, and adresses the Christian God and pantheon.

Now, I would like to focus a moment on 'evil' entities the ancient Hellenes did believe in: ghosts. Ghosts were the people who could not find the entrance to the Underworld or who didn't have the money to pay Kharon for their passage. Those who were not properly buried were also doomed to wander the Earth for a hundred years. Interestingly enough, Hellenic heroes were also considered ghosts and were honored in the same type of rites as other types of ghosts.

The ancient Hellens held festivals in honor of ghosts, and the Theoi that presided over them, so they would be sated and appeased and would not haunt them. Most of these festivals included a holókaustos--a sacrificial offering given in its entirety to the Gods--and were solemn affairs, conducted at night and without an offering of wine.

This fear of spirits and other supernatural entities was named 'deisidaimonia' (δεισιδαιμονία). The ceremonies of riddance were known to the Hellenes as apopompai (ἀποποπμαί), 'sendings away'. There isn't a single word in the English language that conveys the practice. Closest would be, indeed, 'exorcism'.

It is important to note here that these 'exorcisms' weren't performed on people, but on the ghosts themselves and in short, they consisted of rites to ask the Gods (especially Hekate) to keep these unfortunate souls away from their homes and families, because the ghosts could bring misery down upon them. Possession was not part of the fear. Many rites in the ancient Hellenic religion--including monthly ones like the Deipnon--were apotropaic. Many of these rites were also linked to miasma.

Within Hellenic practice, miasma describes the lingering aura of uncleanliness in regards to a person or space through which contact is made with the Gods. Next to piety, being ritually clean is one of the most important things to adhere to within Hellenismos. Severe miasma needs to be cleansed by the Gods, and these rites were apotropaic in nature.

The answer to the question at hand is thus that it depends on the time period and your definition. Strictly speaking, the ancient Hellenes in general did not believe in possession, but did have specific rites to ward off the evil and miasmic. Later on, especially in cult worship, some forms of demon possession became a known issue, but by and large, demon possession did not occur until the Roman empire and the rise of Christianity. Perhaps it was a different understanding of the same thing, but the concept would have been foreign to the ancient Hellenes. By extension, exorcisms were too.

If you have a question you would like to ask, you can always contact me through Facebook or e-mail at baring.the.aegis at gmail dot com. I greatly enjoy answering questions so don't hesitate if you are struggling with something.