Classical differential geometry can be encoded in spectral data, such as Co
nnes' spectral triples, involving supersymmetry algebras. In this paper, we
formulate non-commutative geometry in terms of supersymmetric spectral dat
a. This leads to generalizations of Connes' non-commutative spin geometry e
ncompassing noncommutative Riemannian, symplectic, complex-Hermitian and (H
yper-) Kahler,geometry. A general framework for non-commutative geometry is
developed from the point of view of supersymmetry and illustrated in terms
of examples. In particular, the noncommutative torus and the non-commutati
ve 3-sphere are studied in some detail.