One of the passages used most for justifying the doctrine of Original Sin is Romans 5:12-21:
Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned-- for sin indeed was in the world before the law was given, but sin is not counted where there is no law. Yet death reigned from Adam to Moses, even over those whose sinning was not like the transgression of Adam, who was a type of the one who was to come. But the free gift is not like the trespass. For if many died through one man's trespass, much more have the grace of God and the free gift by the grace of that one man Jesus Christ abounded for many. And the free gift is not like the result of that one man's sin. For the judgment following one trespass brought condemnation, but the free gift following many trespasses brought justification. If, because of one man's trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ. Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men. For as by the one man's disobedience the many were made sinners, so by the one man's obedience the many will be made righteous. Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, so that, as sin reigned in death, grace also might reign through righteousness leading to eternal life through Jesus Christ our Lord. (Romans 5:12-21)
A key part of this passage that is called out in, for example, Wayne Grudem's Systematic Theology is verses 18-19:
Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men. For as by the one man's disobedience the many were made sinners, so by the one man's obedience the many will be made righteous. (Romans 5:18-19)
Concerning these verses, Grudem states (Systematic Theology, pgs. 494-495):
Here Paul says explicitly that through the trespass of one man "many were made [Gk. katestathesan, also an aorist indicative indicating completed past action] sinners." When Adam sinned, God thought of all who would descend from Adam as sinners. Though we did not yet exist, God, looking into the future and knowing that we would exist, began thinking of us as those who were guilty like Adam. This is also consistent with Paul's statement that "while we were yet sinners Christ died for us" (Rom. 5:8). Of course, some of us did not even exist when Christ died. But God nevertheless regarded us as sinners in need of salvation. The conclusion to be drawn from these verses is that all members of the human race were represented by Adam in the time of testing in the Garden of Eden. As our representative, Adam sinned, and God counted us guilty as well as Adam.
Grudem calls this "inherited guilt" rather than using the terminology for Original Sin, but he means the same thing (Systematic Theology, pg. 494, note 8). You can see from the quote above that this comes directly from the very clear statements in Romans 5:18, "Therefore, as one trespass led to condemnation for all men..." and 19, "For as by the one man's disobedience the many were made sinners..." Too often we can be lulled into the sense that such statements are like math equations, where x+1=5 then x always equals 4. Sucking the verses out of context is not possible if they are like equations because the equation x+1=5 cannot be taken out of context, it stands alone. Likewise it appears that if we read "one trespass led to condemnation for all men" and "by the one man's disobedience the many were made sinners" then we have equations that always lead to the doctrine of Original Sin (where at the very moment we are conceived the guilt from the Sin of Adam is attached to us). The problem comes in when we take into consideration the remainder of the verses. If "one trespass led to condemnation for all men" means that the trespass of Adam is automatically conferred upon each and every one of us then the rest of that verse, which reads, "so one act of righteousness leads to justification and life for all men" means that everyone is saved. Do you see how this works if we read these like equations, that is, as though we are reading a math book? The original equation is "one trespass equals condemnation for all men" but the follow up equation is "one act of righteousness equals justification and life for all men." They negate each other! The same is true for Romans 5:19, which if we read it like a math book states, "one man's [Adam's] disobedience equals many sinners." The second half of the verse, in math book form is, "one man's [Christ's] obedience equals many righteous." Do you see the problem here? If we proof-text Original Sin by making syllogisms out of sub-pieces of sentences in individual verses then Universalism (the idea that everyone is saved) immediately follows. You can't get Original sin out of Romans 5:18-19 without also getting Universalism and since Universalism violates so many parts of the Bible (large swaths of the Old Testament and most of the New Testament) Original Sin is not an acceptable exegesis of Romans 5:18-19.
When it comes to Romans 5, then, the interpretation must be other than Original Sin. That is, the point of the passage is not to prove Original Sin. I think the problem most people have is not understanding what Adam's sin led to. We can understand this if we go back to what God told Adam in the Garden of Eden:
The "Surety of Death" was the punishment that came to Adam as a result of his sin. This Surety of Death is passed down through all generations and we inherit it even today, for we know that we will "surely die" unless Jesus comes before our death. Even if it were possible for us to live a perfect life then we would still "surely die" so we have inherited the punishment that Adam received for his sin. This is different from inheriting sin that we did not commit, which would violate passages like Ezekiel 18 (yeah, the whole chapter, which teaches quite clearly that we are responsible for our own actions). Humanity "surely dies" and so that punishment is still with us, even today, but we are responsible for our own actions and do not inherit some sin from our forefathers that we did not commit ourselves.And the LORD God commanded the man, saying, "You may surely eat of every tree of the garden, but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die." (Genesis 2:16-17)