First, let it be said that Jesus is not recorded in the gospels as saying anything that can be construed as particularly supportive of the doctrine of Original Sin.  Jesus did talk about sin, to be sure (and n.b., dear readers, I am not disputing the reality of sin, just the doctrine of Original Sin).  Probably the closest he came to tackling the idea of inherited sin is the pericope of Jesus healing a man born blind in John 9:1-12, which begins:

As he went along, he saw a man blind from birth. His disciples asked him, “Rabbi, who sinned, this man or his parents, that he was born blind?”

“Neither this man nor his parents sinned,” said Jesus, “but this happened so that the works of God might be displayed in him. As long as it is day, we must do the works of him who sent me. Night is coming, when no one can work. While I am in the world, I am the light of the world.’

Having said this, he spit on the ground, made some mud with the saliva, and put it on the man’s eyes. “Go,” he told him, “wash in the Pool of Siloam” (this word means “Sent”). So the man went and washed, and came home seeing. (TNIV)

As usual with Jesus, his primary point seems to be subvert the conventional wisdom of the day.  His interlocuters assume that the man’s blindness is a direct result of either A) his own sin, or B) his parents’ sin.
 

Option A indicates that Jesus’ questioners did consider it possible that sin was present in an infant: this man was born blind, and they wonder if it was his own sin that caused his blindness; since we can assume that they did not mean that he volitionally sinned in utero, they are asking Jesus about some inherited sin passed down through the generations.

Option B indicates that the man’s blindness is a direct result of his parents’ sins, whatever they may be.

The ideas of inherited and generational sin were topics of debate among rabbis in Jesus’ day, so it isn’t that surprising that Jesus’ disciples would want him to weigh in on the matter.  The Hebrew Bible itself is ambivalent on this notion.  In Exodus 34, just after Moses chiseled the commandments,

And [the LORD] passed in front of Moses, proclaiming, “The LORD, the LORD, the
compassionate and gracious God, slow to anger, abounding in love and
faithfulness, maintaining
love to thousands, and forgiving wickedness, rebellion and sin. Yet he
does not leave the guilty unpunished; he punishes the children and
their children for the sin of the parents to the third and fourth
generation.”

Yet in Ezekiel 18, the Lord repeatedly announces through the prophet that the sins of the parents are not imputed to the children,

“Yet you ask, ‘Why does the son not share the guilt of his father?’
Since the son has done what is just and right and has been careful to
keep all my decrees, he will surely live.
The one who sins is the one who will die. The child will not share the
guilt of the parent, nor will the parent share the guilt of the child.
The righteousness of the righteous will be credited to them, and the
wickedness of the wicked will be charged against them.”

We can see why the disciples’ want Jesus opinion on the matter. 

But, as usual, Jesus doesn’t pick A or B, but instead replies, “Neither this man nor his parents sinned, but this happened so that the works of God might be displayed in him.” A bit of an odd response, and one that has implications for questions about theodicy, but surely not one that supports the notion of inherited guilt (Augustine) or total depravity (Calvin).

In sum, Jesus speaks several times about the reality and consequences of sin, but he does not seem to support the doctrine of Original Sin as it developed in the Early Church and the Reformation.

So, what say you, dear readers?  How does Jesus support or not support the doctrine of Original Sin?