We present results for the SM and MSSM Higgs-boson production cross sections at the Tevatron and the LHC. The SM cross sections are a compilation of the state-of-the-art theoretical predictions. The MSSM cross sections are obtained from the SM ones by means of an effective coupling approximation, as implemented in FeynHiggs. Numerical results have been obtained in four benchmark scenarios for two values of tan beta, tan beta = 5, 40.