Christianity says that people DON'T have powers, God does. Jesus had powers because he was the son of God. If some other fellow has them, then he's either:
a) Son of God
b) Son of Satan (anti-christ, anybody?)
c) Proof against christianity
d) A fraud
I tend towards (d).
Christianity does state that people are given divine talents and abilities (this could be translated into powers). Some of our talents are without repentance [meaning that we do not have to change our ways and come to Christ], and others are given to us by the authority of Christ our Lord and the Father. Prophetic abilities, the ability to pray for ones healing [God ultimately heals the person in the end, but at the request of an authorized believer], divine visions, my new found understanding and knowledge of the word [whether you choose to believe it or not] could all be considered powers. Some of us are here to set the way for the coming of the Lord, others to mislead and steal from the Lord.
There are also false prophets, and antichrist, which will perform miracles on behalf of the Evil one. Satan is in control of this world, and he knows that half truths are more powerful than full blown lies, so it only makes sense that he would heal people in an attempt to lead people away from the Lord.
The prophecies however have not been fulfilled, and when the Lord returns to this world you will know it. May God have mercy on our souls?