Some couples want to try living together to see how they get on together before committing to marriage. Other times, they simply don't have the option to get married. For example, same-sex couples have marriage rights only in a handful of American states, and at one time interracial marriage was socially forbidden.
Living together makes economic sense, as a couple can share the costs of utility bills and other expenses between them. In the lead-up to an expensive wedding, cohabitation could mean big savings. In some cases, marriage can affect taxation and social security benefits, so couples choose to live together rather than marry.