We have conducted a survey for Cepheid variables in the Sculptor group spiral NGC 300. Based on observations obtained with the Wide-Field Camera at the 2.2 m ESO/MPI telescope during 29 nights spread over a 5.3 month interval, 117 Cepheids and 12 Cepheid candidates were found, which cover the period range from 115 to 5.4 days. We present a catalog that provides equatorial coordinates, period, time of maximum brightness, and intensity mean B and V magnitudes for each variable, and we show phased B and V light curves for all the Cepheids found. We also present the individual B and V observations for each Cepheid in our catalog. During our search we rediscovered all 18 previously known Cepheids and confirmed the Cepheid nature of three Cepheid candidates from the previous photographic survey of Graham. Star V4 in Graham's list, classified by him as an eclipsing binary, turns out to be another Cepheid. We find very good agreement between our photometry and that obtained by Freedman et al. from ground-based CCD data for common stars. Using the earlier data together with our new data, we were able to significantly improve the periods for 15 Cepheids in our sample. One of the Cepheids with earlier observations shows evidence for a change of its period over the last 26 years. The Cepheids delineate the spiral arms of NGC 300, and a couple of them were detected very close to the center of the galaxy. From the color-magnitude diagram of NGC 300 constructed from our data, we expect that our Cepheid detection is nearly complete for variables with periods longer than about 10 days. We present plots of the period-luminosity relations in the B and V bands obtained from our data, which clearly demonstrate the presence of a Malmquist bias for periods shorter than about 10 days. A thorough discussion of the distance to NGC 300 will be presented in a forthcoming paper, which will include the analysis of photometry in longer wavelength bands. Based on observations obtained with the 2.2 m ESO/MPI telescope at the European Southern Observatory.