First of all, yes, possession is a real thing. But this need clarification.
There are several "kinds" of possession, for example, if you ever try a ouija board(I hope neither of you do), keep in mind that one of your friends is moving the glass, because he has been possessed.
In order for the glass to move, a random spirit possess someone, it tends to be the weakest soul.
This would explain why we all heard stories about people having horrible experiences using a ouija board, but it doesn't always end in a frightening, cruel, strong possession, sometimes the spirit lets the people alone when things are finished.
As to the demonic possession we all know about, well. They exist, but they are not very usual. And as you would expect, people who are possessed will keep it as a big secret.
I've seen cases of people being possessed, and the things which happened to them were not normal at all, nor could be explained as a "mind malfunction". For example, their eyes randomly changed their colours.