Femtosecond transient absorption spectroscopy and microscopy were employed to study exciton dynamics in suspended and Si3N4 substrate-supported monolayer and few-layer MoS2 2D crystals. Exciton dynamics for the monolayer and few-layer structures were found to be remarkably different from those of thick crystals when probed at energies near that of the lowest energy direct exciton (A exciton). The intraband relaxation rate was enhanced by more than 40 fold in the monolayer in comparison to that observed in the thick crystals, which we attributed to defect assisted scattering. Faster electron-hole recombination was found in monolayer and few-layer structures due to quantum confinement effects that lead to an indirect-direct band gap crossover. Nonradiative rather than radiative relaxation pathways dominate the dynamics in the monolayer and few-layer MoS2. Fast trapping of excitons by surface trap states was observed in monolayer and few-layer structures, pointing to the importance of controlling surface properties in atomically thin crystals such as MoS2 along with controlling their dimensions.