The study of radio pulsars at the highest time resolution is currently limited by the capability of the signal detection system to accept a wide-bandwidth signal, and to sample the data rapidly enough. We describe a new instrument for pulsar research which utilizes baseband recording at 400 Mbit s(-1) to achieve bath a high bandwidth and a high sustained data rate. The wide bandwidth digital recording (WBDR) system is based on a custom analog/digital VLSI digitizer operating at 50 MHz, and a commercial digital cassette tape recorder. Signal analysis is performed entirely in software, using a massively parallel computer. Since we record a representation of the electric vector of the pulsar emission, the instrument is very flexible, and the data can be analyzed in several modes in software. We can synthesize the software equivalent of a conventional hardware filterbank, and we have implemented a ''coherent dedispersion'' algorithm, which yields a sample time of 10 ns. The combination of a wide bandwidth and sustained data rate make this instrument a unique and powerful tool for pulsar astronomy. Our instrument is particularly well-suited to searches for millisecond pulsars at low frequency, in directions where pulsed signals are strongly dispersed by the interstellar medium. We present results based on dual-polarization test observations in a 600 +/- 25 MHz band at the Owens Valley Radio Observatory 40-m Telescope.