Spontaneous emission is not inherent to an emitter, but rather depends on its electromagnetic environment. In a microcavity, the spontaneous emission rate can be greatly enhanced compared with that in free space. This so-called Purcell effect can dramatically increase laser modulation speeds, although to date no time-domain measurements have demonstrated this. Here we show extremely fast photonic crystal nanocavity lasers with response times as short as a few picoseconds resulting from 75-fold spontaneous emission rate enhancement in the cavity. We demonstrate direct modulation speeds far exceeding 100 GHz ( limited by the detector response time), already more than an order of magnitude above the fastest semiconductor lasers. Such ultrafast, efficient, and compact lasers show great promise for applications in high-speed communications, information processing, and on-chip optical interconnects.