This was a subject I've encountered recently and had to pause for a second. It is a subject that is avoided by many, but with respect to the Word of God, I feel all questions should get an honest answer, using the Word and the Bible.
The reality is that there is a discussion about this in the Bible. Marriage within the family did occur – both Sarah and her sister, Rebekah, were the half-sisters of Abraham (Genesis 20:12). Isaac and Jacob were also married to kinswomen. There was no specific statute at that time that prohibited it. The human gene pool was still very young and God has allowed it. However, things took a turn for the worse.
God's word is very clear in Leviticus 18. He commands you, "None of you shall uncover the nakedness of one of his relatives" (Leviticus 18:6, ESV). He then enumerates particular relationships and refers to such relationships as a defilement, such as sister[s], mother, aunt, daughter-in-law. This was not only a cultural norm. God said: "Abomination" (Leviticus 18:29).
The part of me that is touched by this passage is in the way that God has presented it. He tells us, "Do not defile yourselves in these ways" (Leviticus 18:24). Behind these words there is a protective heart. God was not trying to cut His people down, He was trying to protect them.
This is the standard that is upheld in the New Testament as well. Paul reprimands such a situation in 1 Corinthians 5:1, which refers to a man living with his father's wife, something he considers immoral, even by the standards of the unbelieving world.
So what do I have to gain out of it all? That God's laws are not random. They are filled with wisdom, dignity and love. Close relatives were not to be—so God set the limits and they're there to keep us, our families and generations to come safe.