I would like to quickly point out that not every instance of illness or disease in the New Testament was a result of demon possession:
Mark 1:32-34 (NASB)
32 When evening came, after the sun had set, they began bringing to Him all who were ill and those who were demon-possessed.
33 And the whole city had gathered at the door.
34 And He healed many who were ill with various diseases, and cast out many demons; and He was not permitting the demons to speak, because they knew who He was.
In such examples as the woman with the flow of blood, this was not a case of demon possession.
Now even though I agree that we as a society are more aware of epilepsy and other diseases, this does not at all mean that all such diseases were believed to have been caused by demons. In other words, it seems that demonic possession could manifest itself in ways that looked like diseases.
Matthew 12:22 (NASB)
22 Then a demon-possessed man who was blind and mute was brought to Jesus, and He healed him, so that the mute man spoke and saw.
Here we see that in this instance of demon-possession, it was manifested in the man as blindness and muteness. We see later on that Jesus does heal other blind men, but scripture does not at all say that those other instances of blindness were the result of demon possession (John 9:1-4). Blindness and muteness could have been the result of either natural causes, or a supernatural influence (demonic possession).
As for whether demonic possession in the New Testament still exists in the exact same form today is a question that I have not fully reached a conclusion on. I would certainly agree that demonic influences still exist today, but to say whether full possession still exists is a different question that I have yet to fully study.
What I will say though is that when I see events like the Miami man who was eating another man's face I cannot help but think of demonic influences (and possibly possession). Here is the news article for those who have not heard of it:
Rudy Eugene Identified As Naked Miami Man Who Chewed Victim's Face (VIDEO, PHOTOS)
I would like to quote some interesting parts of that article:
"But Vega said when the police officer yelled at Eugene to back away, the naked man merely raised his head "with pieces of flesh in his mouth," growled, and began chewing again."
"The officer reportedly then shot Eugene once, but Eugene still continued to attack the man's face, prompting the officer to shoot multiple times until he was dead. The shooting and its aftermath were captured on surveillance video from the Miami Herald's parking garage, but police are still trying to piece together details and are asking witnesses to come forward."
"Aguilar says authorities have seen several such cases of delirium in which people
have taken off their clothes, seemingly displayed superhuman strength, and have used their jaws as weapons. One such assault allegedly occurred after the Ultra Music Festival in March when a naked reveler Evan Oberfelder attacked a good samaritan and first responders after being hit by a taxi. 14 police officers were treated for blood exposure or injuries after managing to subdue Oberfelder."
Finally, after reading a bit more about the shooter in the Colorado town of Aurora, it seems obvious that something was wrong both 'mentally' and 'spiritually' with this man. I won't deny the possibility that demonic influences were involved in that man's decision to do what he did. Yet it seems to be very difficult to explain it from a purely natural or psychological perspective (he was a PhD student, no criminal background, seemingly normal parents, etc.). Perhaps there were drugs involved, but nothing has come out yet about that possibility. For that reason I cannot rule out the possibility of demonic influence. Thoughts?