If sex between a husband and wife is not a sin, then why/how are we conceived in sin?
ESV - 5 Behold, I was brought forth in iniquity, and in sin did my mother conceive me.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
What I don't see here is the understanding that David's mother and David were shunned by the family and community, as David was considered a bastard. In Psalms 69:8 David makes reference to this; the phrase translated as "alien" or "stranger" to his brothers is actually a Hebrew term used for bastards and children of adultery.
If you read Jewish history, and even if you carefully read the old testament, it's clear that David's father became concerned about his Moabite blood in the law against Israelites marrying Moabites. At the time of David's conception, his father is said to have ended marital relations with his wife for some time.
In light of this, 51:5 is very likely talking of his mother's adultery. This is generally considered why David is shown throughout his life in the Bible to be hated by family, derided and generally an outcast
I WILL echo another answer, in that Ezek 18:20-32 clearly rebukes original sin. Knowing that salvation on decreases condemnation under the law, we must read the New Testament with this knowledge. Thus, stating the sinfulness of the nature of the world and flesh is just that, observing that we all eventually NEED forgiveness.
There's no need to condemn folks before they sin. Adam and Eve introducing sin is likewise just that, they were the first to sin so that is sin's debut. Nothing automatically implies sin itself is passed on, only the burden of sins and the curse of toiling caused by being thrown out of Eden. That's as far as the New or Old testament explicitly state. Since Ezekiel explicitly rebukes original sin, we must not add anything beyond these simple observations