Common Law Marriage
If you both agree that you're married, and then live together in Texas, and while living together in Texas, represent to others that you're married, then you are. You can fill out a form with the County Clerk called a Declaration and Registration of Informal Marriage so that there's a record, but it's not required.
If you are in a relationship and living together, that doesn't necessarily mean you have an informal marriage. First of all you have to be at least 18 years old while you are living together. Secondly, you both must have agreed that you are married. And finally, you must have told or indicated to others that you are married. Whether you agreed to be married can be a he said/she said debate later if there is a breakup. However, if you stopped living with that person more than two years ago, there is a presumption that no informal marriage existed.
As an aside, note that there is no such thing as an informal or common law divorce. Sometimes a married couple agrees to go their separate ways and not mess with the expense or hassle of getting formally divorced. They just act divorced and pretend that they are. This is not a real divorce. Once you're married, you stay married until either you have a piece of paper signed by the judge that says you're divorced or the other spouse dies.
Disclaimer: This article is intended for information only and is not legal advice. Every situation is unique and you should consult with an attorney regarding your particular circumstances.