We report on a search for the neutral and charged Higgs bosons predicted by models of spontaneous symmetry breaking with more than one Higgs doublet field. No signals are observed. We set model-independent limits on masses or branching ratios of singly and pair-produced neutral and charged Higgs bosons. In addition, we interpret our results in the framework of a general two-doublet Higgs model and the Minimal Supersymmetric extension of the Standard Model.