The photoluminescence decay dynamics of colloidal CdSe, Cu+:CdSe, and CuInS2 nanocrystals have been examined as a function of temperature and magnetic field. All three materials show photoluminescence decay on time scales significantly longer than the intrinsic lifetimes of their luminescent excited states, i.e., delayed luminescence, involving formation of a metastable trapped excited state followed by detrapping to re-form the emissive excited state. Surprisingly, the delayed luminescence decay kinetics are nearly identical for these three very different materials, suggesting they reflect universal properties of the delayed luminescence phenomenon in semiconductor nanocrystals. By measuring luminescence decay over 8 decades in time and 6 decades in intensity, we observe for the first time a clear deviation from power-law dynamics in delayed luminescence. Furthermore, for all three materials, the delayed luminescence decay dynamics are observed to be nearly independent of temperature between 20 K and room temperature, reflecting tunneling as the dominant mechanism for detrapping from the metastable state. A kinetic model is introduced that invokes a log-normal distribution of tunneling rates and reproduces the full range of delayed luminescence decay dynamics well. These findings are discussed in relation to photoluminescence blinking, with which delayed luminescence appears closely associated.