We perform a wide parameter-space search for continuous gravitational waves over the whole sky and over a large range of values of the frequency and the first spin-down parameter. Our search method is based on the Hough transform, which is a semicoherent, computationally efficient, and robust pattern recognition technique. We apply this technique to data from the second science run of the LIGO detectors and our final results are all-sky upper limits on the strength of gravitational waves emitted by unknown isolated spinning neutron stars on a set of narrow frequency bands in the range 200-400 Hz. The best upper limit on the gravitational-wave strain amplitude that we obtain in this frequency range is 4.43x10(-23)