How Can God Love Me?

In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace.  Ephesians 1:7

For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.  John 3:16

One will scarcely die for a righteous person-though perhaps for a good person one would dare even to die-but God shows his love for us in that while we were still sinners, Christ died for us.  
Romans 5:7-8

The measure of God's Love for us is shown by two things.  One is the degree of his sacrifice in saving us from the penalty of our sin.  The other is the degree of unworthiness that we had when he saved us.
We can hear the measure of his sacrifice in the words, "He gave his only son". (John 3:16)  We also heart in the word "Christ".  This is a name based on the Greek title Christos or "Anointed One," or "Messiah."  It is a term of great dignity.  The Messiah was to be the king of Israel.  He would conquer the Romans and bring peace and security to Israel.  In sum, then, the person that God sent to save sinners was his divine Son, his only Son, and the Anointed king of Israel--indeed the king of the world (Isaiah 9:6-7)
When we add to this consideration the horrific death by crucifixion that Christ endured, it becomes clear that the sacrifice the Father and the Son made was indescribably great--even infinite, when you consider the distance between the divine and the human.  But God chose to make this sacrifice to save us.
The measure of his love for us increases still more when we consider our unworthiness.  "Perhaps for a good person one would dare even to die---but God shows his love for us in that while we were still sinners, Christ dies for us" (Romans 5:7-8).  We deserved divine punishment, not divine sacrifice.
I have heard it said, "God didn't die for frogs. So he was responding to our value as humans."  This turns grace on its head.  We are worse off than frogs.  They have not sinned.  They have not rebelled and treated God with the contempt of being inconsequential in our lives. God did not have to die for frogs.  They aren't bad enough.  We are.  Our debt is so great only divine sacrifice can pay it.
There is only one explanation for God's sacrifice for us.  It is not us.  It is "the riches of his grace"(Ephesians 1:7).  It is all free.  It is not a response to our worth.  It is the overflow of his infinite worth.  In fact, that is what divine love is in the end: a passion to enthrall undeserving sinners, at great cost, with what will make us supremely happy forever, namely, his infinite beauty.
John Piper