There are actually some Christian groups that believe that the devil has already been defeated (and so has no power, etc.) They are certainly in the minority, and often tend to be more Universalist in their beliefs. Many of them point to Jesus' death and resurrection as the fulfillment of all prophecy, including the ones about the devil's defeat.
These folks use verses like the following to "backup" their belief that Satan was already defeated:
1 John 3:8 - "For this purpose the Son of God was manifested, that he might destroy the work of the devil."
John 12:31 - "Now is the judgment of this world; now the ruler of this world will be cast out." (this takes place during the crucifixion)
Romans 8:31-34 - "Who can bring a charge against God's elect? It is God who justifies.Who is he who condemns?" (the argument here plays off the idea of Satan being the adversary / prosecutor in the Old Testament)
Here's a blog posting from someone who believes this -- gives a bunch more Biblical references. Not everyone makes the argument the same way, but the general ideas are often the same.
It is interesting though how various groups have wrestled with that exact issue -- some say the devil's already been beaten, some say God's just biding his time until the end of the world, some others say that God can't defeat Satan yet (for various reasons), ... and on and on.
