Certain universal C*-algebras for *-semigroups will be introduced. Some basic examples, and ones that occur in describing the C*-algebra of a partial isometry, will be discussed. The latter is a Cuntz- Pimsner C*-algebra associated with a C*-correspondence, and can be viewed as a form of crossed product C*-algebra for an action by a completely positive map. The C*-algebras involved occur as universal C*-algebras associated with contractive *-representations, and complete order *-representations, of certain *-semigroups.