We introduce a new survey of massive stars in the Galaxy and the Magellanic Clouds using the Fibre Large Array Multi-Element Spectrograph (FLAMES) instrument at the Very Large Telescope (VLT). Here we present observations of 269 Galactic stars with the FLAMES-Giraffe Spectrograph (R ≃ 25 000), in fields centered on the open clusters NGC 3293, NGC 4755 and NGC 6611. These data are supplemented by a further 50 targets observed with the Fibre-Fed Extended Range Optical Spectrograph (FEROS, R = 48 000). Following a description of our scientific motivations and target selection criteria, the data reduction methods are described; of critical importance the FLAMES reduction pipeline is found to yield spectra that are in excellent agreement with less automated methods. Spectral classifications and radial velocity measurements are presented for each star, with particular attention paid to morphological peculiarities and evidence of binarity. These observations represent a significant increase in the known spectral content of NGC 3293 and NGC 4755, and will serve as standards against which our subsequent FLAMES observations in the Magellanic Clouds will be compared.