A notion of a wild \(*\)-algebra is applied to the study of certain classes of linear operators on a Hilbert space – algebraic operators, partial isometries, \(n\)-centered operators (intermediate between centered and weakly centered ones), and also to families of operators satisfying some relations. A \(*\)-algebraic version of the Morita equivalence and localization are used to prove the wildness of the unitary classification problems for algebraic partial isometries, \(n\)-centered partial isometries, pairs of self-adjoint operators connected by braid group relations.