Before Abraham Was, I Am
The one thing more striking than Jesus' "I Am" statements followed by some metaphor of divinity, is when Jesus follows the statement "I Am" with nothing, simply letting it stand alone as a name-claim. It is a claim to be the self-existent, eternal, covenant-keeping God that in Genesis 1 created the universe.
We come across just such a statement from Jesus -- which R.C. Sproul calls "Jesus' greatest self-disclosure" -- in John 8:58: "before Abraham was, I am."
Don't miss the fact that Jesus is not just claiming to be older than some ancient dead guy. Jesus is saying to Jews, who had just referenced Abraham as their father and therefore there source of security and identity: "Before Abraham was, I am."
What is your "Abraham"? Something or someone that you are banking on, from which you draw your identity. The first thing perhaps that comes to your mind as your safety net when you're afraid, or that brings you happiness when you're down, or that reassures you when you feel guilty. About that thing or person, Jesus says, "Before that, before him or her, before your gifts or your sin or your loved one, I am."