Investigations that probe defects one at a time offer a unique opportunity to observe properties and dynamics that are washed out of ensemble measurements. Here we present confocal fluorescence measurements of individual defects in Al-doped ZnO nanoparticles and undoped ZnO sputtered films that are excited with sub-bandgap energy light. Photon correlation measurements yield both antibunching and bunching, indicative of single-photon emission from isolated defects that possess a metastable shelving state. The single-photon emission is in the range ~560 – 720 nm and typically exhibits two broad spectral peaks separated by ~150 meV. The excited state lifetimes range from 1 – 13 ns, consistent with the finite-size and surface effects of nanoparticles and small grains. We also observe discrete jumps in the fluorescence intensity between a bright state and a dark state. The dwell times in each state are exponentially distributed and the average dwell time in the bright (dark) state does (may) depend on the power of the exciting laser. Taken together, our measurements demonstrate the utility of a single-molecule approach to semiconductor defect studies and highlight ZnO as a potential host material for single-defect based applications.