  Three sets of exactly solvable one-dimensional quantum mechanical potentials
are presented. These are shape invariant potentials obtained by deforming the
radial oscillator and the trigonometric/hyperbolic P\"oschl-Teller potentials
in terms of their degree \ell polynomial eigenfunctions. We present the entire
eigenfunctions for these Hamiltonians (\ell=1,2,...) in terms of new orthogonal
polynomials. Two recently reported shape invariant potentials of Quesne and
G\'omez-Ullate et al's are the first members of these infinitely many
potentials.
