"Behold, I was shapen in iniquity; and in sin did my mother conceive me." (Psalm 51:5)
In "God's Word for Today" David Woods writes:

We have no indication from scripture that David's parents committed adultery or fornication when he was conceived. Rather, every indication we have is that his parents were in a loving, faithful relationship. Verse 5 points to a deeper truth. Indeed, David would probably say that we all have been “shapen in iniquity.” How is this true?
We are all born with a nature corrupted by carnality, an inclination to rebel against God in order to worship self as god.

Source: Studies in the Psalms: Adult Teacher's Insights, page 47.