Over half the 3CRR sample of radio galaxies and quasars has been observed in X-rays with ROSAT pointed observations, and we present results from these observations, discussing many of the sources in detail. The improved spatial resolution of ROSAT over earlier missions allows a better separation of the nuclear and extended components of the X-ray emission. We investigate the relationship between nuclear X-ray and core radio luminosity and show that our results support a model in which every radio galaxy and quasar has a beamed nuclear soft X-ray component directly related to the radio core. We report evidence for rich cluster environments around several powerful quasars. These X-ray environments are comparable to those of high-redshift radio galaxies.