We present the results of a search for gravitational waves associated with
154 gamma-ray bursts (GRBs) that were detected by satellite-based gamma-ray
experiments in 2009-2010, during the sixth LIGO science run and the second and
third Virgo science runs. We perform two distinct searches: a modeled search
for coalescences of either two neutron stars or a neutron star and black hole;
and a search for generic, unmodeled gravitational-wave bursts. We find no
evidence for gravitational-wave counterparts, either with any individual GRB in
this sample or with the population as a whole. For all GRBs we place lower
bounds on the distance to the progenitor, under the optimistic assumption of a
gravitational-wave emission energy of 10^-2 M c^2 at 150 Hz, with a median
limit of 17 Mpc. For short hard GRBs we place exclusion distances on binary
neutron star and neutron star-black hole progenitors, using astrophysically
motivated priors on the source parameters, with median values of 16 Mpc and 28
Mpc respectively. These distance limits, while significantly larger than for a
search that is not aided by GRB satellite observations, are not large enough to
expect a coincidence with a GRB. However, projecting these exclusions to the
sensitivities of Advanced LIGO and Virgo, which should begin operation in 2015,
we find that the detection of gravitational waves associated with GRBs will
become quite possible.