My answer, originally posted to Quora
I don't know about other countries, but yes, an adult can be legally adopted in many states in the USA, including California. The criteria for allowing adult adoption varies state to state.
Adult adoption creates a legal parent-child relationship between two adults, with all the rights and responsibilities of a biological parent-child relationship, including inheritance rights. See http://www.saclaw.org/pages/adult-adoption.aspx for more details.