You can claim people as dependents on your income taxes even if they're not related to you. That includes a girlfriend or a boyfriend, or even the girlfriend or boyfriend of one of your children. However, an unrelated individual must first meet several conditions to qualify as a dependent.
The tax code recognizes a "qualifying child" and a "qualifying relative" as eligible dependents. Anyone who is unrelated to you must meet the Internal Revenue Service definition of a qualifying relative for you to claim that person as a dependent. This is the case regardless of the person's age. Despite the name, a family relationship is not required to be a qualifying relative.
A boyfriend or girlfriend must meet four conditions for you to claim that person as a qualifying relative. The first is the "not a qualifying child test." Essentially, you cannot claim someone as a dependent if that person could be claimed as a dependent child on anyone else's tax return. The second condition requires that the person be a member of your household for the entire year. The third is that you must have paid more than half of the person's living expenses. Finally, the person cannot have income in excess of the IRS's personal exemption amount. As of 2015, that was $4,000.