The doctrine of the imputation of Adam's sin means that when Adam first sinned, that sin (and its blame) was rightly regarded by God to be our sin as well. John Piper writes:

The problem with the human race is not most deeply that everybody does various kinds of sins—those sins are real, they are huge and they are enough to condemn us. Paul is very concerned about them. But the deepest problem is that behind all our depravity and all our guilt and all our sinning, there is a deep mysterious connection with Adam whose sin became our sin and whose judgment became our judgment. (John Piper, "Adam, Christ, and Justification: Part 1")

God ordains that that there be a union of some kind that makes Adam's sin to be our sin so that our condemnation is just. ("Adam, Christ, and Justification: Part 5")

The biblical basis for this doctrine of imputed sin is discussed thoroughly in John Piper's five sermons on Romans 5:12-21. Here we will simply seek to summarize some of the primary evidence from this text.

Sin Entered the World Through One Man
First, Paul states in 5:12 that all sinned in Adam: "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." Paul seems to be equating the "because all sinned" with "through one man sin entered into the world."

Sin is Not Imputed Where There is no Law
Second, in verses 13-14 Paul adds a clarification which confirms that he does indeed have the imputation of Adam's sin in view in the phrase "because all sinned" rather than our individual sins. He states: "For until the Law sin was in the world, but sin is not imputed when there is no law. Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come." In other words, Paul concedes that personal sin was prevalent in the world before Moses ("until the Law sin was in the world..."). But he adds that these personal sins were not the ultimate reason people died in that time period: "But sin is not imputed when there is no law. Nevertheless death reigned from Adam until Moses." As Piper summarizes:

People died even though their own individual sins against the Mosaic law were not the reason for dying; they weren't counted. Instead, the reason all died is because all sinned in Adam. Adam's sin was imputed to them. (John Piper, "Adam, Christ, and Justification: Part 2")

Death Reigned Even Over Those Who Did Not Sin Like Adam
Third, Paul's statement at the end of verse 14 further clarifies that he does not have personal sins in view as the reason for human death: "Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam." Piper notes:

In other words, yes Paul concedes that there are other kinds of laws before the Mosaic Law, and yes people broke those laws, and yes, one could argue that these sins are the root cause of death and condemnation in the world. But, Paul says, there is a problem with that view, because death reigned "even over those who had not sinned in the likeness of the offense of Adam." There are those who died without seeing a law and choosing to sin against it.

Who are they? I think the group of people begging for an explanation is infants. Infants died. They could not understand personal revelation. They could not read the law on their hearts and choose to obey or disobey it. Yet they died. Why? Paul answers: the sin of Adam and the imputation of that sin to the human race. In other words, death reigned over all humans, even over those who did not sin against a known and understood law. Therefore, the conclusion is, to use the words of verse 18: "through one transgression there resulted condemnation to all men." (Ibid)

So the purpose of verses 13 and 14 are to clarify verse 12 in this way:

At the end of verse 12 the words, "death spread to all men, because all sinned" mean that "death spread to all because all sinned in Adam." Death is not first and most deeply because of our own individual sinning, but because of what happened in Adam. (Ibid)

Paul's Emphasis Upon the One Transgression
Fourth, at least five times in the following verses Paul says that death comes upon all humans because of the one sin of Adam:

Verse 15: by the transgression of the one the many died

Verse 16: the judgment arose from one transgression resulting in condemnation

Verse 17: by the transgression of the one, death reigned through the one

Verse 18: through one transgression there resulted condemnation to all men

We are all condemned not ultimately because of our individual sins, but because of one sin (verse 18). We die not ultimately because of personal sins, but because of Adam's one transgression (verse 17). It is not ultimately from our personal sins that we die, but rather "by the transgression of the one the many died." Paul states over and over again that it is because of one sin that death and condemnation belong to us all. In other words, we are connected to Adam such that his one sin is regarded as our sin and we are worthy of condemnation for it.

The Direct Statement of Verse 19
Fifth, verse 19 provides us with a direct statement of imputation:

For as through the one man's disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous.

Paul here says that we are made sinners by the sin of Adam. Due to his disobedience, we are regarded as sinners. We cannot take "made sinners" here to be referring to original sin in which we become inherently sinful because it is paralleled with "made righteous." The phrase "made righteous" in this context is referring to the great truth of justification. Justification does not concern a change in our characters, the infusion of something inherent in us. Rather, it involves a change in our standing before God. In justification, God declares us righteous because He imputes to us the righteousness of Christ--not because He makes us internally righteous (cf. 2 Corinthians 5:21). Thus, when Paul says "made righteous" here, he means "imputed with righteousness" not "infused with righteousness." Since "made sinners" is paralleled with "made righteous," it must also be referring to imputation. Thus, Paul is saying that we are all made sinners in the sense that we are imputed with Adam's sin.

Further Resources

John Piper, "Adam, Christ, and Justification"

John Murray, The Imputation of Adam's Sin

John Murray, The Epistle to the Romans, 5:12-21.

Douglas Moo, The Epistle to the Romans, 5:12-21.