In the course of a systematic investigation of proton-induced reactions for p energies between 800 and 2600 MeV, the target elements O, Mg, Al, Si, Ca, Ti, V, Mn, Fe, Co, Ni, Cu, Zr, Rh, Nb, Ba and Au were irradiated with 800 MeV protons at LAMPF/Los Alamos National Laboratory, and with 1200, 1600 and 2600 MeV protons at Laboratoire National Saturne/Saclay. The 1600 MeV irradiations covered in addition the target elements C, N, Rb, Sr, Y. The study was designed to measure production cross sections of radionuclides by γ-spectrometry and by accelerator mass spectrometry and of stable rare gas isotopes by conventional mass spectrometry. A detailed analysis of secondary particle fields was performed for targets of different thicknesses. Corrections for interferences by secondaries were made on the basis of secondary particle spectra as calculated by the code HET in the form of the HERMES code system and experimental and theoretical excitation functions of p- and n-induced reactions. Here, about 700 cross sections for the production of radionuclides from target elements Z ≤ 29 (Cu) by more than 200 reactions are presented. In addition, cross sections for the production of stable He and Ne isotopes from iron at a proton energy of 600 MeV are given. Together with earlier work of our group, there now exists a consistent set of excitation functions from threshold energies up to 2600 MeV. A comparison of the new data with earlier measurements from other authors exhibited a considerable lack of reliability for many of the earlier data. On the basis of the new data, the quality of existing semiempirical formulas for the calculation of spallation cross sections is discussed. In a more physical approach, the production of residual nuclides is calculated in the framework of an INC/E model using Monte Carlo techniques for energies between 100 MeV and 5 GeV and compared with the experimental results.