Believe them or not, cases of demonic possessions have persisted since the dawn of religion. Road Tickle blog has an intriguing post about 4 strange cases of demonic possession.
For example, take a look at this one of Anneliese Michel (1976, actually - not exactly the Middle Ages), which was the basis of the horror movie The Exorcism of Emily Rose:
She soon had her suspicions confirmed when voices told her she was damned. The voices were paired with hallucinations during prayer. Though originally marked up to her epilepsy her behavior became increasingly bizarre; the young began eating coal, spiders, and licking up her own urine. While the 1970s aren’t exactly the bastion of the medical age it’s safe to assume that this stopped being epilepsy after the second spider-urine smoothie.
After journeying on a pilgrimage with another woman, it was determined that Anneliese was possessed when she was unable to pass by an icon of Christ. An exorcist was granted permission to attempt to exorcise the demon believed to posses her. This continued for almost a year in tandem with psychiatric treatments. Eventually Anneliese chose to rely strictly on the the exorcism sessions over any other medical treatments. These sessions proved to do very little, and on July 1st, 1976, Anneliese died in her sleep. An autopsy proved the cause of death to be starvation; during the exorcisms Anneliese refused to eat, choosing to die as a means to atone for the wayward youth.
Previously on Neatorama: The Stories Behind Four Exorcisms