  A stable model category is a setting for homotopy theory where the suspension
functor is invertible. The prototypical examples are the category of spectra in
the sense of stable homotopy theory and the category of unbounded chain
complexes of modules over a ring. In this paper we develop methods for deciding
when two stable model categories represent `the same homotopy theory'. We show
that stable model categories with a single compact generator are equivalent to
modules over a ring spectrum. More generally stable model categories with a set
of generators are characterized as modules over a `ring spectrum with several
objects', i.e., as spectrum valued diagram categories. We also prove a Morita
theorem which shows how equivalences between module categories over ring
spectra can be realized by smashing with a pair of bimodules. Finally, we
characterize stable model categories which represent the derived category of a
ring. This is a slight generalization of Rickard's work on derived equivalent
rings. We also include a proof of the model category equivalence of modules
over the Eilenberg-Mac Lane spectrum HR and (unbounded) chain complexes of
R-modules for a ring R.
