If you are not married, then one type of relationship you should understand is called a domestic partnership. Domestic partnerships are similar to marriage and may apply to unmarried couples as well as those who are in same-sex relationships.
In the past, most domestic partnerships were made up of people in same-sex relationships, but that is not the case today. Today, people can opt for a marriage instead, regardless of their gender and the gender of the person that they wish to marry.
A domestic partnership is still an option for those who live together and who have a common life but do not wish to be married. This relation is not the same as getting married, but it does have some of the benefits of marriage. A domestic partnership is also known as a civil union in some places, but it is not always the same thing.
It is important to register your domestic partnership at a designated courthouse or government office. Domestic partners gain a number of legal benefits including coverage on family health insurance policies, the right to family leave if they or a family member is sick, the right to visitation in hospitals and jails and the right to bereavement leave. These are not all of the same benefits that people obtain when they are married, but it is a substantial improvement over seeking no benefits through the law at all. If you retain a relationship with no legal documentation, then you will typically not have the right to the benefits listed above, regardless of the situation.