  We perform an extensive survey of rare and exclusive few-body decays --
defined as those with branching fractions $\mathcal{B} \lesssim 10^{-5}$ and
two or three final particles -- of the Higgs, Z, W bosons, and the top quark.
Such rare decays can probe physics beyond the Standard Model (BSM), constitute
a background for exotic decays into new BSM particles, and provide precise
information on quantum chromodynamics factorization with small nonperturbative
corrections. We tabulate the theoretical $\mathcal{B}$ values for almost 200
rare decay channels of the four heaviest elementary particles, indicating the
current experimental limits in their observation. Among those, we have computed
for the first time ultrarare Higgs boson decays into photons and/or neutrinos,
H and Z radiative decays into leptonium states, radiative H and Z
quark-flavour-changing decays, and semiexclusive top-quark decays into a quark
plus a meson, while updating predictions for a few other rare H, Z, and top
quark partial widths. The feasibility of measuring each of these unobserved
decays is estimated for p-p collisions at the high-luminosity Large Hadron
Collider (HL-LHC), and for $e^+e^-$ and p-p collisions at the future circular
collider (FCC).
