Here is a brief list of some of the areas in a persons life that a demon can affect. Please note that every time you find somebody struggling or facing one of the areas below, it's not necessarily a demon, but it's not uncommon to find a demon behind these things.

Compulsive sinning against your will: Addictions, uncontrollable anger, lust, urges to murder or commit suicide, etc.

Compulsive sinning against your will: Satan caused Judas to dishonestly gain money at the cost of Jesus' death. There were two men who were possessed with demons who were said to have uncontrollable anger problems (Matthew 8:28), so much that nobody could get near them they were so fierce. King Saul also became very angry after he picked up an unclean spirit, and even tried to murder David (1 Samuel 19:9-10)! Babylon was known as a habitation of devils (Revelations 18:2) and it was well known for sins of every kind, indicating that demons can and do promote sin in a person's life. Canaan is also known to be a cursed nation, and was known for their problems with sin as well. Notice it was the curse that came, THEN the problem with sin and not the other way around.

Self-mutilation is a sin because it's harming our bodies which are temples of the Holy Ghost, and we find the man with the legion roaming the tombs cutting himself uncontrollably. Compulsive behavior is known to be demonic.  Mark 5:2,5, "And when he was come out of the ship, immediately there met him out of the tombs a man with an unclean spirit... And always, night and day, he was in the mountains, and in the tombs, crying, and cutting himself with stones."  In the ministry of deliverance, many people are set free from all kinds of compulsive sinning, even pornography addictions and compulsive masturbation. If it's compulsive and you've tried everything to stop, but you can't... there seems to be a compulsive force 'driving' you to sin, then there may very well be a demon that needs to be driven out. It is true that we have been set free from the bondage of sin, but there's a big difference between the bondage of sin, and being in bondage to demons and their way of affecting you is driving you to sin.

Mental torment: Fear, depression, irrational heaviness in the soul, hearing voices in the mind, hearing auditable voices that nobody else hears, compulsive thoughts, insanity, mental illness, etc. Obsessive irrational worry is almost always a demon. People who are scared stiff over the unpardonable sin are in need of counseling and likely deliverance.

Fear and depression - irrational heaviness in the soul: King Saul was tormented with fear and depression by an evil spirit. 1 Samuel 16:14, "Now the Spirit of the LORD had left Saul, and the LORD sent a tormenting spirit that filled him with depression and fear." (NLT) The Bible also speaks of a spirit of heaviness in Isaiah 61:1,3, where it's speaking of how Jesus came to preach deliverance from such a spirit and give us a garment of praise in exchange. There are a lot of people today who suffer from irrational fears, depression, headaches, nightmares, etc. from demon spirits and after a successful deliverance they are set free.

Emotional problems: Unable to get close to other people, sensing rejection for no reason, irrational emotional breakdowns, etc. Often more then just casting out demons is needed in this category, inner healing must also take place as well as tearing down strongholds.

Physical health problems: Arthritis, cancer, HIV, and a host of other illnesses are almost always caused by evil spirits. If it cannot be easily cured, then it's almost always a spirit that is causing it.

Physical health problems: The woman with the spirit of infirmity, for example, was bound by a spirit of infirmity (Luke 13:11) and as a result, she couldn't lift herself up, she was crippled over. Arthritis is found to be demonic by many ministers today. Job suffered physical affliction from evil spirits by means of boils all over his body (Job 2:7). Matthew 9:32-33 speaks of a man who was possessed with an unclean spirit that caused him to be unable to speak. Matthew 9:25 also speaks of a deaf spirit, "When Jesus saw that the people came running together, he rebuked the foul spirit, saying unto him, Thou dumb and deaf spirit, I charge thee, come out of him, and enter no more into him."

Occult powers or abilities: Anybody who can tell a fortune, lift an object through levitation, break a solid oak board with their hand, etc. using demonic powers needs a deliverance. Martial arts are known for using demonic powers to break boards, etc. Unnatural strength is a sign of demonic power, such as the man with the legion in the Bible.

Supernatural strength or abilities: The girl with the spirit of divination was able to foretell the future through an evil spirit in Acts 16:16. It is pretty solid proof a person has a demon if they have magical powers, such as the magicians who laid out their staffs and they turned into snakes before Moses in Exodus 7:12. The man with the legion of spirits was known to have superhuman strength in Matthew 5:2-4: "No man could bind him, no, not with chains: Because that he had been often bound with fetters and chains, and the chains had been plucked asunder by him, and the fetters broken in pieces: neither could any man tame him."

Unnatural desires and feelings: Sexual attraction towards animals, unnatural sexual desires, unusually strong attractions towards somebody who is married, past lover, etc. can indicate soul ties and demonic bondage. 

Unhealthy obsessions: Obsessions with things such as death like the man in Mark 5:3 had ("Who had his dwelling among the tombs") clearly demonstrates a demonic bondage. Usually obsessions with items of darkness, death, occult, demons, etc. is a sign that something is wrong.

Experiencing the demonic: Most often (not always, but usually) when people are visited by demons, hearing them, seeing them, etc., they are in need of a deliverance.

Ancestors have similar problems: If both you and one or more of your ancestors have the same kind of problem(s), then there may be a generational spirit at work.

Constant calamities in one's life: Job is a good example of what the demonic kingdom can do in a person's life. He had an almost endless list of calamities take place in his life due to an unclean spirit. Job greatly feared such calamities coming upon him (Job 3:25), and did not trust God to protect Him in those areas. This is why I believe God allowed Satan to enter into his life and play havoc on everything he owned, including his own body. Why would a loving God cause His servant to go through so much, just for the sake of 'proving' something to Satan? I don't think it really lines up with God's loving nature towards His people. In Deuteronomy 27, there's a list of things that can cause a person to come under a curse, and in chapter 28, it tells us what kind of problems a curse can cause in a person's life. Not every time a person is under a curse means they have to have demons driven out, but it's certainly something to look into and get freed from.

Obsessions: Driving interests in the occult, demons, and creatures of the dark such as wolves, owls, etc. can indicate a demonic bondage. Obsession with death is almost a sure sign of demonic bondage.

Compulsive behavior: Compulsive behavior such as cutting is a Biblical symptom of demonic bondage.

Mental health problems and insanity: In Matthew 17:15, a boy is said to be a lunatic as a result of indwelling demons. The NT Greek word for lunatic is sele.niazomai and means the person is moon struck (mentally not well) or crazy. Mental problems are clearly shown in other parts in the Bible as well, including the man with the legion in Matthew 5:2-5, "And when he was come out of the ship, immediately there met him out of the tombs a man with an unclean spirit, Who had his dwelling among the tombs; and no man could bind him, no, not with chains: Because that he had been often bound with fetters and chains, and the chains had been plucked asunder by him, and the fetters broken in pieces: neither could any man tame him. And always, night and day, he was in the mountains, and in the tombs, crying, and cutting himself with stones." Does that sound like somebody who's in their right mind to you? What would somebody in their right mind be doing roaming the tombs? This tells me that there was a spirit of death involved, which gave him exceeding interest in the dead. Who in their right mind would be roaming the tombs day and night crying and cutting themselves with stones? When Jesus cast those demons out, the man was said to have been "in his right mind" once again (verse 15).