We observe strong spontaneous emission modification of individual InAs Quantum Dots (QDs) in a 2D photonic crystal with a modified, high-Q single defect cavity. Resonant QDs see an increased emission rate, while off-resonant QDs show up to five-fold decrease of emission rate compared to QDs in bulk semiconductor as their local density of optical states (LDOS) is diminished in the photonic crystal. In both cases, photon correlation measurements demonstrate antibunching behavior and prove that the experiments are performed on a single emitter. We simulate QD emission behavior in a photonic crystal and find good agreement. These results represent the first demonstrations of single photon emission from photonic crystal cavity-coupled QDs.