We observe large spontaneous emission rate modification of individual InAs Quantum Dots (QDs) in 2D a photonic crystal with a modified, high-Q single defect cavity. Compared to QDs in bulk semiconductor, QDs that are resonant with the cavity show an emission rate increase by up to a factor of 8. In contrast, off-resonant QDs indicate up to five-fold rate quenching as the local density of optical states (LDOS) is diminished in the photonic crystal. In both cases we demonstrate photon antibunching, showing that the structure represents an on-demand single photon source with pulse duration from 210 ps to 8 ns. We explain the suppression of QD emission rate using Finite Difference Time Domain (FDTD) simulations and find good agreement with experiment.