We present three-dimensional simulations of the core-collapse of massive rotating and non-rotating progenitors performed with the general relativistic neutrino hydrodynamics code CoCoNuT-FMT and analyse their explosion properties and gravitationalwave signals. The progenitor models include Wolf-Rayet stars with initial helium star masses of 39 M and 20 M , and an 18 M red supergiant. The 39 M model is a rapid rotator, whereas the two other progenitors are non-rotating. Both Wolf-Rayet models produce healthy neutrino-driven explosions, whereas the red supergiant model fails to explode. By the end of the simulations, the explosion energies have already reached 1.1 × 10 51 erg and 0.6 × 10 51 erg for the 39 M and 20 M model, respectively. The explosions produce neutron stars of relatively high mass, but with modest kicks. Due to the alignment of the bipolar explosion geometry with the rotation axis, there is a relatively small misalignment of 30 • between the spin and the kick in the 39 M model. In terms of gravitational-wave signals, the massive and rapidly rotating 39 M progenitor stands out by large gravitational-wave amplitudes that would make it detectable out to almost 2 Mpc by the Einstein Telescope. For this model, we find that rotation significantly changes the dependence of the characteristic gravitational-wave frequency of the f-mode on the proto-neutron star parameters compared to the nonrotating case. The other two progenitors have considerably smaller detection distances, despite significant low-frequency emission in the most sensitive frequency band of current gravitational-wave detectors due to the standing accretion shock instability in the 18 M model.