We have measured cold inelastic collisions between neutral ground-state titanium atoms: collisions that cause transitions between the different magnetic sublevels of the $[3{d}^{2}4{s}^{2}]{^{3}F}_{2}$ ground state of $^{50}\text{T}\text{i}$, as well as collisions that cause transitions between the fine-structure levels of the $[3{d}^{2}4{s}^{2}]{^{3}F}_{J}$ electronic ground state. Both processes occur with large rate coefficients, as would be expected from titanium's anisotropic electronic potential.