Molecular dynamics simulation results are reported for single-file self-diffusion in pores of infinite and finite length. The model system involves moderately dense, nonovertaking, hard-sphere fluids in cylindrical pores, and the particle mobility is investigated as a function of time and pore length. It is shown that, while stationary Fickian diffusion in infinitely long pores with diffusely reflecting pore walls is nonexistent, a diffusivity may be defined for single-file pores of finite length. For pores of moderate length, it is also demonstrated that the self-diffusion coefficient scales as 1/root L where L is the pore length.