We report a systematic study on the crystal growth of the rare-earth titanates $R_2$Ti$_2$O$_7$ ($R$ = Gd, Tb, Dy, Ho, Y, Er, Yb and Lu) and Y-doped Tb$_{2-x}$Y$_x$Ti$_2$O$_7$ ($x$ = 0.2 and 1) using an optical floating-zone method. High-quality single crystals were successfully obtained and the growth conditions were carefully optimized. The oxygen pressure was found to be the most important parameter and the appropriate ones are 0.1--0.4 MPa, depending on the radius of rare-earth ions. The growth rate is another parameter and was found to be 2.5--4 mm/h for different rare-earth ions. X-ray diffraction data demonstrated the good crystallinity of these crystals. The basic physical properties of these crystals were characterized by the magnetic susceptibility and specific heat measurements.