Demon possession is not an uncommon occurrence. It's not a myth or superstition or a made up belief to stir up fear. During the time of Jesus' earthly ministry, "they brought to Him many who were demon-possessed." (Matthew 8:16b, EMTV) The key word is "many". Jesus healed a lot of people from sickness, but He did not think it unusual that people would want freedom from possession by evil spirits either.
Sickness itself is not by its nature a result of possession, but demons can create physical abnormalities when they inhabit us. "Then some people brought Jesus a man possessed by a demon. The demon made the man blind and unable to talk." (Matthew 12:22a, GW) A biblical version of Helen Keller had resulted in that man because he was possessed. So sickness and disease can at times be symptomatic, or a side-effect, of possession.
Another "side-effect" of demonic possession is obtaining a paranormal ability such as the practices studied in article V on supernatural phenomena.
One day when we were going to the place of prayer, a female servant met us. She was possessed by an evil spirit that told fortunes. – Acts 16:16, GW
Lastly, it's also possible to be possessed by more than one evil spirit at a time:
"When an evil spirit comes out of a person, it goes through dry places looking for a place to rest. But it doesn't find any. Then it says, 'I'll go back to the home I left.' When it comes, it finds the house swept clean and in order. Then the spirit goes and brings along seven other spirits more evil than itself. They enter and take up permanent residence there. In the end the condition of that person is worse than it was before." – Luke 11:24-26, GW
If a person does not allow Jesus Christ to take control of their life after being set free from demonic possession, it is possible they will be inhabited by even more evil spirits. And as the above verses say, that person's condition is not looking good.
Learn what authority Jesus Christ really has to set us free from oppression or possession by demons in the next article: Understanding demons Bible-style VIII, Christ's power over demons.
You can also read this series from the beginning: Understanding demons Bible-style, Introduction