This report summarizes the final results from the OPAL collaboration on searches for neutral Higgs bosons predicted by the Minimal Supersymmetric Standard Model (MSSM). CP-conserving and for the first time at LEP CP-violating scenarios are studied. New scenarios are also included, which aim to set the stage for Higgs searches at future colliders. The results are based on the data collected with the OPAL detector at e+e- centre-of-mass energies up to 209 GeV. The data are consistent with the prediction of the Standard Model with no Higgs boson produced. Model-independent limits are derived for the cross-sections of a number of event topologies motivated by predictions of the MSSM. Limits on Higgs boson masses and other MSSM parameters are obtained for a number of representative MSSM benchmark scenarios. For example, in the CP-conserving scenario mhmax where the MSSM parameters are adjusted to predict the largest range of values for mh at each tanbeta, and for a top quark mass of 174.3 GeV, the domain 0.7 < tanbeta < 1.9 is excluded at the 95% confidence level and Higgs boson mass limits of mh > 84.5 GeV and mA > 85.0 GeV are obtained. For the CP-violating benchmark scenario CPX which, by construction, enhances the CP-violating effects in the Higgs sector, the domain tanbeta<2.8 is excluded but no universal limit can be set on the Higgs boson masses.