We have developed and tested a photonic high speed analog data recording system that, when compared with conventional oscilloscope-based systems, offers greater economy, higher bandwidth, electrical isolation, and compactness. The basis of this approach is to record analog photonic signals rather than analog electrical signals. A key component is a prototype High Speed Multi-Channel Data Recorder (HSMCDR). It uses a picosecond streak camera with a digital readout to record multiple fiber-optic data channels, and a dedicated microcomputer to reduce and process that data. To record signals from analog electrical sensors, laser diode transmitters provide an interface to the HSMCDR. Interactive software written for the HSMCDR separates, calibrates, and plots up to 20 waveforms in the customary amplitude versus time format. We describe the HSMCDR, its performance, applications in pulsed power experiments, and its impact in diagnostic technology.