  We have probed the fragmentation dynamics in a bent triatomic molecule,
water, a non-planar molecule, methanol, and a planar ring-structured molecule,
benzene, using 100 fs duration pulses of linearly and circularly polarized,
infrared, intensity-selected laser light. At laser intensities larger than
10$^{15}$ W cm$^{-2}$, the yield of singly and multiply charged atomic
fragments from these molecules is suppressed when the light is circularly
polarized. At lower intensities, the fragment ion yield is not significantly
polarization dependent. This hitherto-unobserved intensity dependent effect of
the polarization state of light on the fragmentation dynamics is rationalized
using a simple electron rescattering model. Circular polarization switches
"off" electron rescattering and leads to suppression of multiple ionization and
molecular fragmentation. Moreover, the degree of suppression is dependent upon
the amount of energy transfer from the optical field to the molecule: the
larger the energy transfer that is required for a particular fragmentation
channel, the more marked is its suppression when circular polarization is used.
