I think that demon possession is biblical. Jesus obviously believed in it. He drove out demons from the man called legion (Mark 5:1-20) He drove a demon from a boy after his own transfiguration (Luke 9:37-45). Many more examples can be listed. Some like to spiritualize these historical events, saying that these "demons" are just symbolic. Others say that Jesus talks about demons so as to accomodate how his contemporaries thought about demons. These do not work. In the gospels demons speak to Jesus and he talks back to them. No, these demons are real and they are evil. Paul talks about evils spiritual powers which have authority "in this dark world" (Ephesians 5:11). Daniel describes evil angels. We can go on almost indefinitely. These are not symbolic. They are real.
Would a loving God allow demons to exist and to "possess" or otherwise negatively influence people he loves? The answer, apparently is yes. I believe that demons, and even Satan, are angels or other beings who have chosen to rebel against God. God choses, from his love, to give us free will. Apparently, according to the Bible, angelic beings have some sort of free will as well. Satan and his demons try to influence us. That is the biblical picture. Again, apparently, according to the Bible, one of the ways demons work is to "possess" people. It is hard for us to be sure exactly what this means, but it surely is not a good thing for us. This does not disprove God’s love or his soveriegnty, it proves his power and his love.
Are there mental disorders which can produce symptoms which are, at first glance, similar to those described associated with demon possession in the New Testament? The answer is yes. Schizophrenia and other psychotic disorders which have been carefully studied do, at times, produce symptoms which on the surface have some similarities to demon possession as it is described in the Bible. Some have seen similarity between the behavior of the boy in Luke 9:37-45 and the symptoms of epilepsy. Perhaps the boy suffered from epilepsy. However, if Jesus says that he has a demon and if Jesus was able to heal him, I accept the Biblical evidence as sufficient to say that this was more than just a psychological/neuropathology. We should hesitate to assume that the descriptions of demon possession are the same as that of known psychological syndromes. It would be quite speculative to conclude that the man called Legion had a set of symptoms which matches a scientifically-studied psychological syndrome.
What about demon possession today? That is the hard question. It is one not answered in an unambiguous way in the Bible. Why do we not see demon possession in the Western world. Or, putting it more carefully, why is it non-existent or at least relatively rare in the Western world? Why is demon possession more prevalant in parts of the world such as Africa and Indonesia? Is it merely because these people are more superstitious, or it is because demons actually have greater freedom of action in these countries? These are difficult questions for which I have no ready answer. With you, I am quite skeptical of reports of demon possession. However, I believe it is not wise to be hyper-skeptical. If we absolutely deny the reality of demon possession today, how are we to explain that it existed during the ministry of Jesus? We can look for proof-texts such as Revelation 20:2, which talks about Satan being bound. Perhaps this is why we see few if any demons today. It seems to me that in order to establish this as a doctrine, more scriptural evidence may be needed.
How should we respond to people who claim to be possessed by a demon? To be honest, I am not sure. I believe we should be extremely skeptical. It is very unlikely that this person is correct that he or she is indeed possessed by a demon. It is far more likely that he or she is having serious emotional or psychological issues. However, I believe you should hesitate to simply tell your friend that he or she is deceived. This situation should be handled with care and with compassion. You should do some research. You should, if possible, encourage your friend to seek professional psychological help. Do not declare him or her to be crazy or absolutely for sure decieved about the demon possession, but I believe you should not encourage this highly unlikely conclusion. If absolutely nothing is helpful, after a long time and great effort, you might want to find someone who is an expert on the question of demons possession, but I believe it is virtually 100% for sure that you will not end up doing that. Show your friend love, compassion, strong spiritual convictions. Offer him or her Christian discipling. Call him or her to repent of sins (but not necessarily of psychological symptoms which may not be in his or her complete control. If this does not help, you should seek input from a maturee, spiritual person you trust to help you analyze and think about the situation.
I have some good news for you. We at ARS are planning an entire conference next June of the question of Christianity and the Paranormal. Demon possession will be one of our major topics. Perhaps you can plan on attending this conference or buying the DVD of the conference afterward. We will delve more deeply into the topic at the conference. Sorry that I do not have hard-and-fast answers for you, but I will leave the final analysis to you.