We present high resolution UVES+VLT spectroscopic observations of 61 stars in the extended blue horizontal branches of the Galactic globular clusters NGC 1904 (M79), NGC 2808, NGC 6093 (M80), and NGC 7078 M15). Our data reveal for the first time the presence in NGC 1904 of a sizable population of fast (v sin(i) >= 20 km/s) horizontal branch (HB) rotators, confined to the cool end of the EHB, similar to that found in M13. We also confirm the fast rotators already observed in NGC 7078. The cooler stars (T_eff < 11,500 K) in these three clusters show a range of rotation rates, with a group of stars rotating at ~ 15 km/s or less, and a fast rotating group at ~ 30 km/s. Apparently, the fast rotators are relatively more abundant in NGC 1904 and M13, than in NGC 7078. No fast rotators have been identified in NGC 2808 and NGC 6093. All the stars hotter than T_eff ~ 11,500 K have projected rotational velocities vsini< 12 km/s. The connection between photometric gaps in the HB and the change in the projected rotational velocities is not confirmed by the new data. However, our data are consistent with a relation between this discontinuity and the HB jump.