Hello Sister LibertyLady ... this is a great question. I think if we remove (from the Bible) from the question, it will generate even more responses.
My first thought was of our Ancestors, who used "jumping the broom" as an indication that they were married. This is probably not found in the Bible, but the marriage was just as real.
I've heard some say that because they love someone so much, are committed to them, they consider themselves "married," even though they do not have a "marriage license."
There are even "common law marriages" that are based simply on the fact that you've lived together as a couple for some amount of time.
I think, in polygamous relationships, the "wives" that follow the first wife, may not have any "legal" ground to stand on, but consider themselves just as married as the first wife, since this country does not recognize such unions.
I think too, that some men call extra women in their life, "wives," in an attempt to bring honor to what may be extramarital affairs.
I wonder, in historic Africa, what constituted "marriage?" I'm sure as large as Africa is, there were many different ways to recognize "marriage," and few if any were based on the Bible.
Great Topic Sister!
Destee