For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
The Biblical references given have to do with relationships between the couple and God. There are no "legal" requirements according to Scripture.
Today, marriage is a legal term and not a Biblical one. The word "marriage" did not come into our language until the 13th or 14th century. The Hebrew and Greek terms have to do with relationships, not the institution of marriage as we know it today. Respect (union), honor, love and submission are characteristics of the Christian marriage as stated by Mr. Houdmann above. A man and woman do not have to be legally married to be spiritually "married" according to scripture. There is no legal (government) requirement for marriage in Scripture.
Romans 7:2 has to do with a woman being bound to one man. She cannot be bound to more than one man. The man, on the other hand does not have that same requirement in Scripture. I cannot find where a man can only have 1 wife. The requirement of only 1 wife has to do with being a bishop. (1 Timothy 3:2)
If a man is already joined with a woman and lays with another woman, he must take her into his household as another wife with the same privileges as any other wife.
The benefits of legal marriage are many and have nothing to do with a Christian marriage. The benefits of a Christian marriage far outweigh the benefits of a civil marriage if both are committed to having Jesus centered in their lives. A Christian marriage is a covenant whose vows should never be broken. Things go sour with that covenant is violated.