What does the bible say about marriage to a relative?

In The Bible, a man is forbidden to marry the following:

Daugher

Stepchildren

Aunt

Sister or half-sister

Stepsisters

Daughter-in-law

Sister-in-law

Granddaughter

Step-granddaughter

Cousins were not included in the list. It can be found in Leviticus chapter 18. This does not mean it is legal in the state in which you live. Also, if you are Catholic, the practice was banned by Pope Gregory I.
As far as I know cousins were left out, but many are not allowed to marry.
Leviticus 18:6 says "No one is to approach any close relative to have sexual relations. I am the LORD."

The Old and New Testament did not have any strict prohibitions against marrying non-biological relatives. Leviticus is referring to blood relatives when it mentions "close relatives".

The bad part about marrying a blood/genetically close relative is that you cannot have children because they will be "messed up". They can be born without limbs, have brain damage and other genetic problems or even rare diseases. When you see cases of cousins marrying each other in the past or in the Bible you are not really told they were not blood relatives. But, you can bet they were not blood relatives.

For instance: You can marry a cousin who is one by marriage but not by blood (except in states where it is outlawed completely). If your mother has a brother-in-law with a sister-in-law or cousin you could marry their off spring. They are only related by marriage and not by blood.

You could not marry any of the offspring of your mother or father's biological relatives. Read the story of Ruth in the Bible. It is in the index under "Ruth". She marries her mother-in-law Naomi's cousin Boaz. You can see why she was able to marry him once you read the story.