The possibility that chemical reactions may be controlled by tailored femtosecond laser pulses has inspired recent studies that take advantage of their short pulse duration, comparable to intramolecular dynamics, and high peak intensity to fragment and ionize molecules. In this article, we present an experimental quest to control the chemical reactions that take place when isolated molecules interact with shaped near-infrared laser pulses with peak intensities, ranging from 10(13) to 10(16) W/cm(2). Through the exhaustive evaluation of hundreds of thousands of experiments, we methodically evaluated the molecular response of 16 compounds, including isomers, to the tailored light fields, as monitored by time-of-flight mass spectrometry. Analysis of the experimental data, taking into account its statistical significance, leads us to uncover important trends regarding the interaction of isolated molecules with an intense laser field. Despite the energetics involved in fragmentation and ionization, the integrated second-harmonic generation of a given laser pulse (I-SHG), which was recorded as an independent diagnostic parameter, was found to be linearly proportional to the total ion yield (I-MS) generated by that pulse in all of our pulse shaping measurements. Order of magnitude laser control over the relative yields of different fragment ions was observed for most of the molecules studied; the fragmentation yields were found to vary monotonically with I-MS and/or I-SHG When the extensive changes in fragmentation yields as a function of I-MS were compared for different phase functions, we found essentially identical results. This observation implies that fragmentation depends on a parameter that is responsible for I-MS and independent from the particular time-frequency structure of the shaped laser pulse. With additional experiments, we found that individual ion yields depend only on the average pulse duration, implying that coherence does not play a role in the observed changes in yield as a function of pulse shaping. These findings were consistently observed for all molecules studied (p-, m-, o-nitrotoluene, 2,4-dinitrotoluene, benzene, toluene, naphthalene, azulene, acetone, acetyl chloride, acetophenone, p-chrolobenzonitrile, N,N-dimethylformamide, dimethyl phosphate, 2-chloroethyl ethyl sulfide, and tricarbonyl-[eta 5-1-methyl-2,4-cyclopentadien-1-yllmanganese). The exception to our conclusion is that the yield of small singly-charged fragments resulting from a multiple ionization process in a subset of molecules, were found to be highly sensitive to the phase structure of the intense pulses. This coherent process plays a minimal role in photofragmentation; therefore, we consider it an exception rather than a rule. Changes in the fragmentation process are dependent on molecular structure, as evidenced in a number of isomers, therefore femtosecond laser fragmentation could provide a practical dimension to analytical chemistry techniques.