Would it have been possible for Jesus to sin? I think most, if not all of us, agree that Jesus did not sin.  However, the devil tempted Jesus, at least in the wilderness, prior to Jesus' public ministry (Matthew 4:1-11).  Does this mean it would have been possible for Jesus to sin?  Or was the devil just too stupid to realize his efforts were futile?
Yes
John 10:18 (NIV)

No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again. This command I received from my Father.

Jesus, in this verse, says that he has the ability to choose whether he laid down his life or not.
Because of this, he had the free will to choose to follow God's wishes or not.  Therefore, yes, he had the ability to sin.

Wow, I thought this was a pretty obvious answer.  Some more concepts to back up this idea:

Perfection does not preclude sin
Adam and Eve were perfect and sinless in the Garden of Eden.  However, they, who knew no sin, were tempted and succumbed to sin.  Clearly, perfection and not having previously knowing sin is not a preclusion to actually sinning.

Divinity does not preclude sin
Others claim that because of his divinity--more specifically, his part of the trinity--that he was incapable of sin.  However, John 10:18 (shown above), clearly shows that Jesus himself (not the other members of the trinity) had the authority to choose to sin and go against his Father.  Also, his prayer in the Garden of Gethsemane shows that his will and his father's will were separate.  Since their wills were separate and since he had the ability to choose to sin, it would have been possible for Jesus to have put his will first and chose to go against his father's will.


Therefore, Jesus had true and complete free will and the ability to sin.