In the present Letter we report that a number of polyatomic molecules (M) when irradiated with short pulse lasers <90 fs at 750-790 nm and intensities up to 1015 W cir-2 produce multiply charged parent ions and do not fragment to any great degree. This surprising observation is found in both linear and ring structured molecules and is very similar to the behavior of inert atoms such as xenon under the same irradiation conditions. This is a very different behavior from irradiating with nanosecond pulses at 109 W cm-2 where low-mass fragments dominate the spectrum. For the hydrocarbon molecules presented in this work, there exists an envelope of 2+ ionized peaks, which corresponds to the parent and a number of (M -nH) satellites. This feature is characteristic of these molecules in the intensity region 1014-15 W cm-2 and is interpreted as evidence for tunneling or barrier suppression. Coulomb explosion leading to multiply charged atoms, which is evident for CS2, does not seem to be operating for the larger hydrocarbon molecules.