Using depth-sensing indentation with sub-nanometer displacement resolution, the plastic deformation of a range of materials, including a metallic glass, amorphous selenium, Ni3Al, pure Nb, Al, Cu, and Zn metals, and an Al-Mg alloy, has been investigated at room temperature. In amorphous selenium, even the sub-nanometer displacement resolution of the nanoindentation technique cannot reveal any strain burst during deformation at room temperature. In all other metals studied, what may appear to be smooth load-displacement curves at macroscopic scale during indentation deformation in fact turn out to consist of a continuous series of random bursts of the nanometer scale. The occurrence probability of the bursts is found to decrease at increasing burst size. In all of the crystalline metals and alloys studied, the size distribution of the strain bursts seems to follow an exponential law with a characteristic length scale. The absence of the self-organized critical behavior is likely a result of the small size of the strained volume in the nanoindentation situation, which gives rise to a constraint of a characteristic strain. In the metallic glass sample, due to the limited range of the burst sizes encountered, whether the deformation bursts follow an exponential or a power-law behavior corresponding to self-organized criticality is inconclusive. From a theoretical viewpoint based on the Shannon entropy, the exponential distribution is the most likely distribution at a given mean burst size, and this is thought to be the reason for its occurrence in different materials.