  We consider the constraints from Supernova 1987A on particles with small
couplings to the Standard Model. We discuss a model with a fermion coupled to a
dark photon, with various mass relations in the dark sector; millicharged
particles; dark-sector fermions with inelastic transitions; the hadronic QCD
axion; and an axion-like particle that couples to Standard Model fermions with
couplings proportional to their mass. In the fermion cases, we develop a new
diagnostic for assessing when such a particle is trapped at large mixing
angles. Our bounds for a fermion coupled to a dark photon constrain small
couplings and masses <200 MeV, and do not decouple for low fermion masses. They
exclude parameter space that is otherwise unconstrained by existing
accelerator-based and direct-detection searches. In addition, our bounds are
complementary to proposed laboratory searches for sub-GeV dark matter, and do
not constrain several "thermal" benchmark-model targets. For a millicharged
particle, we exclude charges between 10^(-9) to a few times 10^(-6) in units of
the electron charge; this excludes parameter space to higher millicharges and
masses than previous bounds. For the QCD axion and an axion-like particle, we
apply several updated nuclear physics calculations and include the energy
dependence of the optical depth to accurately account for energy loss at large
couplings. We rule out a hadronic axion of mass between 0.1 and a few hundred
eV, or equivalently bound the PQ scale between a few times 10^4 and 10^8 GeV,
closing the hadronic axion window. For an axion-like particle, our bounds
disfavor decay constants between a few times 10^5 GeV up to a few times 10^8
GeV. In all cases, our bounds differ from previous work by more than an order
of magnitude across the entire parameter space. We also provide estimated
systematic errors due to the uncertainties of the progenitor.
