The VLT-FLAMES Tarantula Survey (VFTS) is an ESO Large Programme that has obtained multi-epoch optical spectroscopy of over 800 massive stars in the 30 Doradus region of the Large Magellanic Cloud (LMC). Here we introduce our scientific motivations and give an overview of the survey targets, including optical and near-infrared photometry and comprehensive details of the data reduction. One of the principal objectives was to detect massive binary systems via variations in their radial velocities, thus shaping the multi-epoch observing strategy. Spectral classifications are given for the massive emission-line stars observed by the survey, including the discovery of a new Wolf-Rayet star (VFTS 682, classified as WN5h), 2' to the northeast of R136. To illustrate the diversity of objects encompassed by the survey, we investigate the spectral properties of sixteen targets identified by Gruendl & Chu from Spitzer photometry as candidate young stellar objects or stars with notable mid-infrared excesses. Detailed spectral classification and quantitative analysis of the O- and B-type stars in the VFTS sample, paying particular attention to the effects of rotational mixing and binarity, will be presented in a series of future articles to address fundamental questions in both stellar and cluster evolution. Figures 10-12, Tables 5 and 6, and Appendix A are available in electronic form at http://www.aanda.org