We observe large spontaneous emission rate modification of individual InAs quantum dots (QDs) in a 2D photonic crystal with a modified; high- Q single-defect cavity. Compared to QDs in a bulk semiconductor; QDs that are resonant with the cavity show an emission rate increase of up to a factor of 8. In contrast; off-resonant QDs indicate up to fivefold rate quenching as the local density of optical states 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 a pulse duration from 210 ps to 8 ns. We explain the suppression of QD emission rate using finite difference time domain simulations and find good agreement with experiment.