The N14(p,γ)O15 reaction is the slowest reaction of the carbon-nitrogen cycle of hydrogen burning and thus determines its rate. The precise knowledge of its rate is required to correctly model hydrogen burning in asymptotic giant branch stars. In addition, it is a necessary ingredient for a possible solution of the solar abundance problem by using the solar N13 and O15 neutrino fluxes as probes of the carbon and nitrogen abundances in the solar core. After the downward revision of its cross section due to a much lower contribution by one particular transition, capture to the ground state in O15, the evaluated total uncertainty is still 8%, in part due to an unsatisfactory knowledge of the excitation function over a wide energy range. The present work reports precise S factor data at twelve energies between 0.357 and 1.292 MeV for the strongest transition, capture to the 6.79-MeV excited state in O15, and at ten energies between 0.479 and 1.202 MeV for the second strongest transition, capture to the ground state in O15. An R-matrix fit is performed to estimate the impact of the new data on astrophysical energies. The recently suggested slight enhancement of the 6.79-MeV transition at low energy could not be confirmed. The present extrapolated zero-energy S factors are S6.79(0)=1.24±0.11 keV b and SGS(0)=0.19±0.05 keV b.