  Recent observations have revealed an amazing diversity of extremely luminous
supernovae, seemingly increasing in radiant energy without bound. We consider
here the physical limits of what existing models can provide for the peak
luminosity and total radiated energy for non-relativistic, isotropic stellar
explosions. The brightest possible supernova is a Type I explosion powered by a
sub-millisecond magnetar. Such models can reach a peak luminosity of $\rm
2\times10^{46}\ erg\ s^{-1}$ and radiate a total energy of $\rm 4
\times10^{52}\ erg$. Other less luminous models are also explored, including
prompt hyper-energetic explosions in red supergiants, pulsational-pair
instability supernovae, and pair-instability supernovae. Approximate analytic
expressions and limits are given for each case. Excluding magnetars, the peak
luminosity is near $\rm 1\times10^{44}\ erg\ s^{-1}$ for the brightest models.
The corresponding limits on total radiated power are $\rm3 \times 10^{51}\ erg$
(Type I) and $\rm1 \times 10^{51}\ erg$ (Type II). A magnetar-based model for
the recent transient event, ASASSN-15lh is presented that strains, but does not
exceed the limits of what the model can provide.
