Zinc oxide (ZnO) nanorods (NRs) oriented along the crystallographic [001] axis are grown by the hydrothermal method on glass substrates. The ZnO NRs exhibit a broadband (1-2 mu m) near-IR absorption ascribed to the singly charged zinc vacancy V-z(n)-1. The saturable absorption of the ZnO NRs is studied at approximate to 1 mu m under picosecond excitation, revealing a low saturation intensity, approximate to 10 kW/cm(2), and high fraction of the saturable losses. The ZnO NRs are applied as saturable absorbers in diode-pumped Yb (approximate to 1.03 mu m) and Tm (approximate to 1.94 mu m) lasers generating nanosecond pulses. The ZnO NRs grown on various optical surfaces are promising broadband saturable absorbers for nanosecond near-IR lasers in bulk and waveguide geometries.