In Luke's Gospel we hear of Jesus expelling demons. Is demonic possession real, or was it just some form of mental illness? What we can certainly say is that if demons are real, we don't have to worry about them if we trust in Jesus, because Jesus has power over all.
Based on Luke 4:31-37:
Jesus went down to Capernaum, a city in Galilee, and was teaching them on the sabbath. They were astounded at his teaching, because he spoke with authority. In the synagogue there was a man who had the spirit of an unclean demon, and he cried out with a loud voice, ‘Let us alone! What have you to do with us, Jesus of Nazareth? Have you come to destroy us? I know who you are, the Holy One of God.’ But Jesus rebuked him, saying, ‘Be silent, and come out of him!’ When the demon had thrown him down before them, he came out of him without having done him any harm. They were all amazed and kept saying to one another, ‘What kind of utterance is this? For with authority and power he commands the unclean spirits, and out they come!’ And a report about him began to reach every place in the region.
(New Revised Standard Version Bible: Anglicized Edition, copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org)