  Galaxies are missing most of their baryons, and many models predict these
baryons lie in a hot halo around galaxies. We establish observationally
motivated constraints on the mass and radii of these haloes using a variety of
independent arguments. First, the observed dispersion measure of pulsars in the
Large Magellanic Cloud allows us to constrain the hot halo around the Milky
Way: if it obeys the standard NFW profile, it must contain less than 4-5% of
the missing baryons from the Galaxy. This is similar to other upper limits on
the Galactic hot halo, such as the soft X-ray background and the pressure
around high velocity clouds. Second, we note that the X-ray surface brightness
of hot haloes with NFW profiles around large isolated galaxies is high enough
that such emission should be observed, unless their haloes contain less than
10-25% of their missing baryons. Third, we place constraints on the column
density of hot haloes using nondetections of OVII absorption along AGN
sightlines: in general they must contain less than 70% of the missing baryons
or extend to no more than 40 kpc. Flattening the density profile of galactic
hot haloes weakens the surface brightness constraint so that a typical L$_*$
galaxy may hold half its missing baryons in its halo, but the OVII constraint
remains unchanged, and around the Milky Way a flattened profile may only hold
$6-13%$ of the missing baryons from the Galaxy ($2-4 \times 10^{10}
M_{\odot}$). We also show that AGN and supernovae at low to moderate redshift -
the theoretical sources of winds responsible for driving out the missing
baryons - do not produce the expected correlations with the baryonic
Tully-Fisher relationship and so are insufficient to explain the missing
baryons from galaxies. We conclude that most of missing baryons from galaxies
do not lie in hot haloes around the galaxies, and that the missing baryons
never fell into the potential wells of protogalaxies in the first place. They
may have been expelled from the galaxies as part of the process of galaxy
formation.
