  We have searched for planetary companions around 800 pulsars monitored at the
Jodrell Bank Observatory, with both circular and eccentric orbits of periods
between $20$ days and $17$ years and inclination-dependent planetary masses
from $10^{-4}$ to $100\,\mathrm{M}_{\oplus}$. Using a Bayesian framework, we
simultaneously model pulsar timing parameters and a stationary noise process
with a power-law power spectral density. We put limits on the projected masses
of any planetary companions, which reach as low as 1/100th of the mass of the
Moon ($\sim 10^{-4}\,\mathrm{M}_{\oplus}$). We find that two-thirds of our
pulsars are highly unlikely to host any companions above
$2-8\,\mathrm{M}_{\oplus}$. Our results imply that fewer than $0.5\%$ of
pulsars could host terrestrial planets as large as those known to orbit PSR
B1257$+$12 ($\sim4\,\mathrm{M}_{\oplus}$); however, the smaller planet in this
system ($\sim0.02\,\mathrm{M}_{\oplus}$) would be undetectable in $95\%$ of our
sample, hidden by both instrumental and intrinsic noise processes, although it
is not clear if such tiny planets could exist in isolation. We detect
significant periodicities in 15 pulsars, however we find that intrinsic
quasi-periodic magnetospheric effects can mimic the influence of a planet, and
for the majority of these cases we believe this to be the origin of the
detected periodicity. Notably, we find that the highly periodic oscillations in
PSR B0144$+$59 are correlated with changes in the pulse profile and therefore
can be attributed to magnetospheric effects. We believe the most plausible
candidate for planetary companions in our sample is PSR J2007$+$3120.
