The {100}, {110} and {111} surfaces of silicon, germanium and gallium arsenide, cleaned in ultra-high vacuum by heat-treatments alone or by ion-bombardments followed by anneals, were studied with the display-type low-energy electron diffraction technique. Most surface structures reported in the literature by others could be reproduced, namely, Si(111)7, Ge(111)8, GaAs(111)2, and GaAs(100)1. Some, however, could not, namely, Si(111)5 and Ge(111)12. Two unreported structures were found to exist, even simultaneously, on the GaAs{100} surface and six different structures were detected on Si{110} surfaces after annealing treatments at different temperatures. The significance of a "clean" state of semiconductor surfaces, as identified by the observation of low-energy electron diffraction patterns, is discussed.