Encounters with demons have been reported going back thousands of years and up to our current times. The various reports do have many elements in common so that we can see a thread of consistency through the ages.
An excellent definition of a demon comes from the ancient text of First Enoch:
"But now the giants (Nephilim) who are born from the [union of] the spirits and the flesh shall be called evil spirits upon the earth, because their dwelling shall be upon the earth and inside the earth. Evil spirits have come out of their bodies. Because from the day that they were created from the sons of God they became Watchers: their first origin is the spiritual foundation. They will become evil upon the earth and shall be called evil spirits. The dwelling of the spiritual beings of heaven is heaven; but the dwelling of the spirits of the earth, which are born upon the earth, is in the earth." (1 Enoch 15:8-10)
These earth-bound evil spirits are the disembodied spirits of the Nephilim. Genesis 6 tells us that the Nephilim are the offspring of the fallen angels who mated with humans. These Nephilim are later described through the Old Testament as the giants in the land. As the Nephilim died, their souls, an abomination to the Lord, were destined to roam endlessly across the earth, constantly in search of a body to re-inhabit.
[note: the terms evil spirit, unclean spirit and demon are used interchangeably throughout the Bible.]
We see the arrival of demons on the scene in the Old Testament in Deuteronomy. According to this verse they were not always around, which is consistent with the Enochian explanation of their appearing on the earth. This describes the beginnings of encounters between the demons and mankind.
"They sacrificed to demons, which are not God-
gods they had not known,
gods that recently appeared,
gods your fathers did not fear." (Deuteronomy 32:17)
So we see one aspect of the demon/human encounter is one of worship (false, idolatrous worship according to God). This worship was based on fear and appeasement.
Moving forward in time to the New Testament era, we see demons and demon possession in full swing. One aspect of Jesus' ministry, and later his disciples', was the casting out of demons.
One notable example:
"When Jesus got out of the boat, a man with an evil spirit came from the tombs to meet him. This man lived in the tombs, and no one could bind him any more, not even with a chain. For he had often been chained hand and foot, but he tore the chains apart and broke the irons on his feet. No one was strong enough to subdue him. Night and day among the tombs and in the hills he would cry out and cut himself with stones. [...] Then Jesus asked him, "What is your name?" "My name is Legion," he replied, "for we are many." And he begged Jesus again and again not to send them out of the area. The demons begged Jesus, "Send us among the pigs; allow us to go into them." He gave them permission, and the evil spirits came out and went into the pigs." (Mark 5: 2-13)
From this passage we learn that more than one demon can possess a human simultaneously; they impart greater than human strength to that human, not to mention very anti-social behavior; and they apparently crave remaining in a body, ANY body, even that of a pig instead of being cast out to nothing.
Their over-arching desire to inhabit a human body is also seen in this passage:
"When an evil spirit comes out of a man, it goes through arid places seeking rest and does not find it. Then it says, 'I will return to the house [body] I left.' [...] Then it goes and takes with it seven other spirits more wicked than itself, and they go in and live there. And the final condition of that man is worse than the first. "(Matt 12:43-45)
They apparently can only find rest when they inhabit a person, thus driving them to do so constantly. Jesus goes on to explain in the above passage that the demon can return, and with friends, if the inhabited person does not experience a true conversion.
But what about today? Do these human/demon encounters still continue today?
In the fascinating book "Demon Possession" by John L. Nevius, a missionary to remote parts of China, dozens of encounters are described that exactly fit the Biblical model of demons. He collected eye-witness accounts from many missionaries spread throughout the desolate regions of rural China and compiled them.
The behaviors described are remarkably consistent with each other across distances that were never traveled by the local people. The general trend is that a demon would enter a member of a household, causing convulsions, violence and poltergeist-style effects about the house. The person affected almost never had any recall of the event. (The possession usually seemed to be sporadic, not constant. The observers could not tell if the demon left in between "events" or remained, but was "quiet".) Demands, made through the mouth of the entranced victim, would be on the rest of the family for worship of the entity in order to make the effects of its possession less. So frequently within the family and village, systems of worship of the demon were set up in a vain attempt to appease the spirit and release the affected member from his torment. Of course the spirits are liars so the desperation of the family increased. In every case the health of the possessed individual declined, sometimes unto death.
The author made the observation that these encounters almost always happened in rural areas of less developed countries and were not matched in urban areas. This was also the case in Jesus' time though the reason as to why would be speculation.
One possibility is in our modern, sophisticated, urban centers we don't require forced possession. We gleefully invite inhabitation of demons through mediums and channelers. To channel a spirit guide, ascended master, guardian angel (or whatever prettied up word used to describe it) a person must go into a trance or hypnotic-like state giving over control of their mind to another entity. These episodes do not tend to be violent unless the channeler at some point decides to no longer practice the procedure. Then typical demon possession behavior as described earlier will surface (see The Beautiful Side of Evil by Johanna Michaelson).
Reports of demon encounters have occurred throughout history up to our present time. Hollywood-style drama aside, the descriptions of these events remain basically consistent across time and cultures lending credence to a legitimate phenomenon. Though science will never be able to measure such encounters since they are, by definition, not a part of our material world, human experience will attest to the existence of such creatures.