We report the preparations, thermoelectric and magnetic properties, and electronic structures of Cu-Ti-S systems, namely, cubic thiospinel c-Cu1-xTi2S4 (x <= 0.375), a derivative cubic and Ti-rich phase c-Cu1-xTi2.25S4 (x = 0.5, 0.625), and a rhombohedral phase r-CuTi2S4. All samples have the target compositions except for r-CuTi2S4, whose actual composition is Cu1.14Ti1.80S4. All of the phases have n-type metallic character and exhibit Pauli paramagnetism, as proven by experiments and first-principles calculations. The Cu and Ti deficiencies in c-Cu1-xTi2S4 and r-CuTi2S4, respectively, decrease the electron-carrier concentration, whereas the excess of Ti ions in c-Cu1-xTi2.25S4 largely increases it. For r-CuTi2S4, the reduced carrier concentration increases the electrical resistivity and Seebeck coefficient, leading to the highest thermoelectric power factor of 0.5 mW K-2 m(-1) at 670 K. For all of the CuTiS phases, the thermal conductivity at 670 K is 3.55 W K-1 m(-1), where the lattice part of the conductivity is as low as 1 W K-1 m(-1) at 670 K. As a result, r-CuTi2S4 shows the highest dimensionless thermoelectric figure of merit ZT of 0.2. The present systematic study on the Cu-Ti-S systems provides insights into the structural design of thermoelectric materials based on Cu-M-S (M = transition-metal elements).