  Results are presented on searches for standard model and non-standard model
production of a Higgs boson in pbar-p collisions at sqrt{s}= 1.96 TeV with the
CDF II detector at the Fermilab Tevatron. Using data corresponding to 2-3.6
1/fb of integrated luminosity, searches are performed in a number of different
production and decay modes. No excess in data above that expected from
backgrounds is observed; therefore, we set upper limits on the production cross
section times branching fraction as a function of the Higgs boson mass.
