  We report a Monte Carlo study of the effects of {\it fluctuations} in the
bond distribution of Ising spin glasses in a transverse magnetic field, in the
{\it paramagnetic phase} in the $T\to 0$ limit. Rare, strong fluctuations give
rise to Griffiths singularities, which can dominate the zero-temperature
behavior of these quantum systems, as originally demonstrated by McCoy for
one-dimensional ($d=1$) systems. Our simulations are done on a square lattice
in $d=2$ and a cubic lattice in $d=3$, for a gaussian distribution of nearest
neighbor (only) bonds. In $d=2$, where the {\it linear} susceptibility was
found to diverge at the critical transverse field strength $\Gamma_c$ for the
order-disorder phase transition at T=0, the average {\it nonlinear}
susceptibility $\chi_{nl}$ diverges in the paramagnetic phase for $\Gamma$ well
above $\Gamma_c$, as is also demonstrated in the accompanying paper by Rieger
and Young. In $d=3$, the linear susceptibility remains finite at $\Gamma_c$,
and while Griffiths singularity effects are certainly observable in the
paramagnetic phase, the nonlinear susceptibility appears to diverge only rather
close to $\Gamma_c$. These results show that Griffiths singularities remain
persistent in dimensions above one (where they are known to be strong), though
their magnitude decreases monotonically with increasing dimensionality (there
being no Griffiths singularities in the limit of infinite dimensionality).
