Using CCD UBV photometry and spectroscopy, we have investigated the stellar content of NGC 346, the brightest H II region in the SMC. Spectra of 42 stars confirm that 33 are of O type, of which 11 are of type O6.5 or earlier; this is as many early-type O stars as is known in the rest of the SMC. From the spectroscopy and photometry we are able to construct an H-R diagram which is essentially complete down to ~10M_{sun}_. We find an initial mass-function slope {GAMMA}=-1.9, similar to that found for massive stars near the Sun and in the LMC: the presence of six stars in the mass range 40-85M_{sun}_ suggests that the upper-mass limit of the IMF is also not appreciably lower in the SMC than it is in the Galaxy. Our photometry has identified five probable red supergiants of which one was previously known. These stars, plus two B supergiants, are evolved stars of considerably lower mass (15M_{sun}_) than many of the unevolved cluster members. Most of these lower-mass, evolved stars form a spatially distinct subgroup; we believe that NGC 346 thus provides an example of sequential star formation in the SMC. We also have identified a background field population of 5M_{sun}_ stars. We find that the ionizing flux from the hot stars is consistent with the previously known Half nebular luminosity. Finally, we discuss the enigmatic W-R binary HD 5980, which our point-spread-function fitting has identified as a close visual double.