Augustine was the one who popularized this view and I believe he used it in order to excuse his sinful nature. He often uses Romans 7:14-21 to show how Paul wrote about man not having any matter in abstaining from our sinful nature. If one reads Romans 6-8, they can see that Paul was referring to living life in Romans 7 but in Romans 6 and 8 Paul describes living life by Grace which sets us free from the bondage of the law. This allows us to live by a higher standard but frees us from the conflict of not doing what is right. "But now having been freed from sin and enslaved to God, you derive your benefit, resulting in sanctification, and the outcome, eternal life" (Rom 6:22).
Augustine found the chief scriptural support for this idea of "Original Sin" in Romans 5:12.
Quote from: Romans 5:12 (NASB)
Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned.
Augustine's version of this verse contained a mistranslation. Augustine did not read Greek, the original language of the NT, so he used a Latin translation now called the Vulgate. It renders the last half of the verse as "and so death spread to all men, through one man, in whom all men sinned." (quoted in Pelikan, The Emergence of the Catholic Tradition, p. 299) He concluded that "in whom" referred to Adam and that somehow all people had sinned when Adam had sinned. He made Adam a kind of corporate personality who contained the nature of all future men, which he transmitted through his semen. Augustine wrote, "We all were in that one man...already the seminal nature was there from which we were to be propagated." (City of God, 13:14). Thus all of Adam's descendants are both corrupt and condemned because they were present inside of him (as semen) when he sinned. Augustine described sin as something "contracted" and passed through the human race like a venereal disease. Jesus was exempt from original sin since, according to the orthodox, he was conceived without semen.
Ezekiel 18:20 makes it clear that sin is a result of each individual person and is not passed down from generation to generation like Augustine believed.
The soul who sins is the one who will die. The son will not share the guilt of the father, nor will the father share the guilt of the son. The righteousness of the righteous man will be credited to him, and the wickedness of the wicked will be charged against him.