Single crystals of TiO₂ anatase containing 0.22% of Al and traces of V, Zr, Nb, and La were grown by chemical transport reactions employing TeCl₄ as the transporting agent. Electrodes having the (101) face exposed doped by reduction with hydrogen were employed. The electrochemical and photoelectrochemical behavior of a single crystal of anatase were scrutinized for the first time. Properties were compared to those of single-crystal rutile having the (001) face exposed. Impedance analysis established that the flatband potential of anatase (101) is shifted negatively by 0.2 V with regards to that of rutile (001). Interfacial capacitance measurements under forward bias indicate smaller density of surface states on anatase. Photoelectrochemical oxidation of water occurs on both rutile and anatase with incident photon-to-current conversion efficiencies close to unity at λ = 300 nm. From the comparison of U_fb and E_g, it follows that anatase (101) and rutile (001) electrodes differ mainly in the position of the conduction band edge. The complete photoelectrolysis of water to H₂ and O₂ is thermodynamically possible on anatase only. Photosensitized electron injection from adsorbed cis-Ru[L₂(SCN)₂] (L = 2,2‘-bipyridyl-4,4‘-dicarboxylic acid) proceeds with similar efficiency on both types of electrodes. However, light-induced charge separation on the single-crystal electrodes is about three times less efficient compared with nanoscopic anatase films. Anatase (101) is strikingly more active for electrochemical insertion of Li⁺ than rutile (001). The diffusion coefficients for Li⁺ insertion and extraction were estimated to be 2 × 10^-13 and 6 × 10^-13 cm²/s, respectively.