A search is made for charged Higgs bosons predicted by Two-Higgs-Doublet extensions of the Standard Model (2HDM) using electron-positron collision data collected by the OPAL experiment at root s = 189-209 GeV, corresponding to an integrated luminosity of approximately 600 pb(-1). Charged Higgs bosons are assumed to be pair-produced and to decay into q (q) over bar, tau nu(tau) or AW(+/-)*. No signal is observed. Model-independent limits on the charged Higgs-boson production cross section are derived by combining these results with previous searches at lower energies. Under the assumption BR(H-+/- -> tau nu(tau)) + BR(H-+/- -> q (q) over bar) = 1, motivated by general 2HDM type II models, excluded areas on the [m(H +/-), BR(H-+/- -> tau nu(tau))] plane are presented and charged Higgs bosons are excluded up to a mass of 76.3 GeV at 95 % confidence level, independent of the branching ratio BR(H +/- -> tau nu(tau)). A scan of the 2HDM type I model parameter space is performed and limits on the Higgs-boson masses m(H)+/- and m(A) are presented for different choices of tan beta.