Data collected by the OPAL detector at LEP2 energies of sqrt(s)=189-209 GeV, corresponding to a total integrated luminosity of 615 pb^-1, are analysed for possible signals of charged Higgs boson production predicted by Two Higgs Doublet extensions of the Standard Model (2HDM). Charged Higgs bosons are assumed to be pair-produced in electron-positron collisions and to decay into q qbar, tau nu_tau or AW^*. No signal has been observed. Cross-section limits are obtained for the different final state topologies. Excluded areas in the [m_H+- - BR(H+- --> tau nu_tau)] plane are derived assuming BR(H+- --> q qbar) + BR(H+- --> tau nu_tau) = 1. Mass limits in 2HDM type I are calculated including the results of the search for the decay H+- --> AW*.