We place direct upper limits on the amplitude of gravitational waves from 28 isolated radio pulsars by a coherent multidetector analysis of the data collected during the second science run of the LIGO interferometric detectors. These are the first direct upper limits for 26 of the 28 pulsars. We use coordinated radio observations for the first time to build radio-guided phase templates for the expected gravitational-wave signals. The unprecedented sensitivity of the detectors allows us to set strain upper limits as low as a few times 10(-24). These strain limits translate into limits on the equatorial ellipticities of the pulsars, which are smaller than 10(-5) for the four closest pulsars.