We present upper limits on the gravitational wave emission from 78 radio pulsars based on data from the third and fourth science runs of the LIGO and GEO 600 gravitational wave detectors. The data from both runs have been combined coherently to maximize sensitivity. For the first time, pulsars within binary (or multiple) systems have been included in the search by taking into account the signal modulation due to their orbits. Our upper limits are therefore the first measured for 56 of these pulsars. For the remaining 22, our results improve on previous upper limits by up to a factor of 10. For example, our tightest upper limit on the gravitational strain is 2.6×10^-25for PSR J1603−7202, and the equatorial ellipticity of PSR J2124–3358is less than 10^-6. Furthermore, our strain upper limit for the Crab pulsar is only 2.2 times greater than the fiducial spin-down limit.