Actually, looking through the Bible, a good case can be made that, if you have sex with someone, you're married to them then.
So make sure your first time is with who you're gonna stay with forever.
This isn't true as in the case of the Samaritan woman. Jesus encountered her and told her that she has had five "husbands" and the man she has now is not her husband, after she told him she had no husband. (John 4) They weren't married, yet they were clearly living together and having sex. Marriage is a covenant made before witnesses and most importantly, God. It's not something you can simply do in private and simply cross your fingers and hope for the best. Unfortunately you are wrong in saying that having sex makes you married to the person. That's like saying those who are victims of rape are married to the rapist. Sound fair to you? A little sound and biblical exegesis will reveal that sex creates a one-flesh union, but not necessarily marriage. Again, biblically speaking, Jesus attended a traditional wedding in the culture which supports the notion that Jesus saw it as an acceptable marriage.
To simply ignore the "state" as you call it, is setting up some rebellious Christian anarchy, destroying your testimony, and setting yourself up for marital failure.
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Romans 13
Be Subject to Government
1 Every person is to be in subjection to the governing authorities. For there is no authority except from God, and those which exist are established by God.
2 Therefore whoever resists authority has opposed the ordinance of God; and they who have opposed will receive condemnation upon themselves.
3 For rulers are not a cause of fear for good behavior, but for evil. Do you want to have no fear of authority? Do what is good and you will have praise from the same;
4 for it is a minister of God to you for good. But if you do what is evil, be afraid; for it does not bear the sword for nothing; for it is a minister of God, an avenger who brings wrath on the one who practices evil.
5 Therefore it is necessary to be in subjection, not only because of wrath, but also for conscience' sake.
6 For because of this you also pay taxes, for rulers are servants of God, devoting themselves to this very thing.
7 Render to all what is due them: tax to whom tax is due; custom to whom custom; fear to whom fear; honor to whom honor. "
We cannot pick and choose what to obey regarding Scriptural commands, except common sense speaking, if the authority commands that you violate Scripture. It is custom in our country to get married in a ceremony, therefore we have the obligation to do so. This is why common-law isn't a Scriptural idea. Considering the couple isn't considered married until a certain period of time has passed, they are having sex outside of marriage in that instance. I don't see what is so difficult about paying a few bucks to get a license, or having a ceremony with friend's and family. Obedience is the biggest issue here, you can't argue with the above Scripture passage. Testimony is also key.