Energy-straggling distributions of 20- and 49-MeV protons and 80-MeV helium ions have been measured for energy losses of 10 to 92% of the initial kinetic energy. Aluminum and gold absorbers were used, and the residual energy spectra were measured with lithium-drifted silicon semiconductor detectors. Experimental results show very good agreement with the theories of Payne and Tschal\"ar, provided that broadening due to atomic binding is taken into account, and disagreement with the Bohr theory for energy losses greater than 20%. In particular, as the particle beam slows down in the absorber, the variance of the energy distribution increases faster than the absorber thickness traversed, and a degree of skewness (i.e., a low-energy "tail") is introduced at very large energy losses.