  We present an extensive search in the literature and Gaia DR2 for visual
co-moving binary companions to stars hosting exoplanets and brown dwarfs within
200 pc. We found 218 planet hosts out of 938 to be part of multiple-star
systems, with 10 newly discovered binaries and 2 new tertiary stellar
components. This represents an overall raw multiplicity rate of 23.2$\pm$1.6%
for hosts to exoplanets across all spectral types, with multi-planet systems
found to have a lower duplicity frequency at the 2.2$\sigma$ level. We found
that more massive hosts are more often in binary configurations, and that
planet-bearing stars in multiple systems are predominantly the most massive
component of stellar binaries. Investigations of multiplicity as a function of
planet mass and separation revealed that giant planets with masses >0.1 MJup
are more frequently seen in stellar binaries than small sub-Jovian planets with
a 3.6$\sigma$ difference, a trend enhanced for the most massive (>7 MJup)
short-period (<0.5 AU) planets and brown dwarf companions. Binarity was found
to have no significant effect on the demographics of low-mass planets (<0.1
MJup) or warm and cool gas giants (>0.5 AU). While stellar companion mass
appears to have no impact on planet properties, binary separation seems to be
an important factor in the resulting structure of planetary systems. Stellar
companions on separations <1000 AU can play a role in the formation or
evolution of massive close-in planets, while planets in wider binaries show
similar properties to planets orbiting single stars. Finally, numerous stellar
companions on separations <1-3 arcsec likely remain undiscovered to this date.
Continuous efforts to complete our knowledge of stellar multiplicity on
separations of tens to hundreds of AU are essential to confirm the reported
trends and further our understanding of the roles played by multiplicity on
exoplanets.
