Self-imaging of ultrashort-pulsed nondiffracting needle beams, i.e., fringe-free Bessel beams, is analyzed. In contrast to the classical diffractive Talbot effect, pulse revivals with minimum spectral and temporal distortion are obtained. Robustness is further enhanced by self-reconstruction. The high-fidelity pulse transfer enables spatial and temporal multiplexing in free space without the need for a nonlinear medium, even at pulse durations down to the few-cycle range.