Heavy-ion induced nuclear reactions in materials exposed to energetic ions produced from high-intensity (approximately 5 x 10(19) W/cm(2)) laser-solid interactions have been experimentally investigated for the first time. Many of the radionuclides produced result from the creation of "compound nuclei" with the subsequent evaporation of proton, neutron, and alpha particles. Results are compared with previous measurements with monochromatic ion beams from a conventional accelerator. Measured nuclide yields are used to diagnose the acceleration of ions from laser-ablated plasma to energies greater than 100 MeV.