We present new observations of 470 stars using the Fibre Large Array Multi-Element Spectrograph (FLAMES) instrument in fields centered on the clusters NGC 330 and NGC 346 in the Small Magellanic Cloud (SMC), and NGC 2004 and the N11 region in the Large Magellanic Cloud (LMC). A further 14 stars were observed in the N11 and NGC 330 fields using the Ultraviolet and Visual Echelle Spectrograph (UVES) for a separate programme. Spectral classifications and stellar radial velocities are given for each target, with careful attention to checks for binarity. In particular, we have investigated previously unexplored regions around the central LH9/LH10 complex of N11, finding ~25 new O-type stars from our spectroscopy. We have observed a relatively large number of Be-type stars that display permitted Fe II emission lines. These are primarily not in the cluster cores and appear to be associated with classical Be-type stars, rather than pre main-sequence objects. The presence of the Fe II emission, as compared to the equivalent width of Hα, is not obviously dependent on metallicity. We have also explored the relative fraction of Be- to normal B-type stars in the field-regions near to NGC 330 and NGC 2004, finding no strong evidence of a trend with metallicity when compared to Galactic results. A consequence of service observations is that we have reasonable time-sampling in three of our FLAMES fields. We find lower limits to the binary fraction of O- and early B-type stars of 23 to 36%. One of our targets (NGC 346-013) is especially interesting with a massive, apparently hotter, less luminous secondary component.