  Superpartner masses cannot be arbitrarily heavy if supersymmetric extensions
of the standard model explain the stability of the gauge hierarchy. This
ancient and hallowed motivation for weak scale supersymmetry is often quoted,
yet no reliable determination of this upper limit on superpartner masses
exists. In this paper we compute upper bounds on superpartner masses in the
minimal supersymmetric model, and we identify which values of the superpartner
masses correspond to the most natural explanation of the hierarchy stability.
We compare the most natural value of these masses and their upper limits to the
physics reach of current and future colliders. As a result, we find that
supersymmetry could explain weak scale stability naturally even if no
superpartners are discovered at LEP II or the Tevatron (even with the Main
Injector upgrade). However, we find that supersymmetry cannot provide a
complete explanation of weak scale stability, if squarks and gluinos have
masses beyond the physics reach of the LHC. Moreover, in the most natural
scenarios, many sparticles, for example, charginos, squarks, and gluinos, lie
within the physics reach of either LEP II or the Tevatron. Our analysis
determines the most natural value of the chargino (squark) ((gluino)) mass
consistent with current experimental constraints is $\sim$ 50 (250) ((250)) GeV
and the corresponding theoretical upper bound is $\sim$ 250 (700) ((800)) GeV.
