Do ghosts exist? And do they possess incredible supernatural powers?

The word is simply Old English for guest.    So they have no supernatural powers

No. The Bible shows that the dead are unconscious at Ecclesiastes 9:5,10. The demons that  sided with Satan try to get people are still alive as ghosts. That goes back to the original lie that Satan told Eve ,”Ye shall not surely die.”( Genesis 3:5) see jw.org for more.

I have not seen any evidence to suggest they do exist. 

I am not superstitious.

I am a little stitious. 

I do not believe so.  

They exist, but most of them have very limited powers.

No, ghosts don't exist.

They do exist, but the modern ghost mostly watches TV.

I don’t believe that they can’t exist. Some say they are psychological manifestations of our strongest emotions such as guilt, amplified by certain surroundings or situations. Others say they are simply echoes or recordings of past events that took place in an area. Some say they are disembodied souls with sentience and supernatural powers. 

There are no disembodied spirits walking the earth.