Cross sections for the 7Be(p,gamma)8B reaction have been measured for E_c.m.= 0.35-1.4 MeV using radioactive 7Be targets. Two independent measurements carried out with different beam conditions, different targets and detectors are in excellent agreement. A statistical comparison of these measurements with previous results leads to a restricted set of consistent data. The deduced zero-energy S-factor S(0) is found to be 15-20% smaller than the previously recommended value. This implies a 8B solar neutrino flux lower than previously predicted in various standard solar models.