Aims: We analyse a significantly large sample of spectroscopic data to provide a compositional characterization of the near-Earth asteroid population. We present visible and near-infrared spectra of a total of 74 near-Earth asteroids (NEAs) and Mars-crossers (MCs), covering the wavelength region from 0.5 to 2.5 μm. Using spectra of NEAs from other databases to enlarge our sample, and compiling two comparison samples of main belt asteroids (MBs) and ordinary chondrites (OCs), we analyse a total of 79 NEAs, 91 MBs, and 103 OCs. Methods: We obtained our visible and near-infrared spectra using the instruments and the telescopes located at “El Roque de los Muchachos” Observatory, in the island of La Palma (Spain). We compute several diagnostic spectral parameters from the reflectance spectra of NEAs, MBs, and OCs, that are used to infer the mineralogical composition. The distribution of the obtained values are analysed in 2 different parameter spaces. We also apply a robust statistical method based on neuronal networks to those spectral parameters, to compare the NEAs with OCs. Space weathering effects and dynamical and physical properties of NEAs and MBs are also studied. Results: Compositional differences between MBs and NEAs are inferred from the mineralogical analysis. The most remarkable results are: (1) the high olivine content of the NEAs; (2) the compositional similarity between NEAs and a small group of meteorites, the LL ordinary chondrites; and (3) that NEAs are not compositionally similar to OCs, implying that they are not the most likely parent bodies of those meteorites, as has been widely believed. To explain their apparently fresh surfaces (NEAs are on average less red than MBs), a combination of composition and size distribution (NEAs have diameters of some kilometres) should be invoked. Dynamical models applied to our sample of NEAs indicate that most of them originate in the inner part of the main belt, as expected. Appendices are only available in electronic form at http://www.aanda.org