  We argue that current neutron star observations exclude asymmetric bosonic
non-interacting dark matter in the range from 2 keV to 16 GeV, including the
5-15 GeV range favored by DAMA and CoGeNT. If bosonic WIMPs are composite of
fermions, the same limits apply provided the compositeness scale is higher than
~10^12 GeV (for WIMP mass ~1 GeV). In case of repulsive self-interactions, we
exclude large range of WIMP masses and interaction cross sections which
complements the constraints imposed by observations of the Bullet Cluster.
