Context. The fraction of binary stars is an important ingredient to interpret globular cluster dynamical evolution and their stellar population. Aims: We investigate the properties of main-sequence binaries measured in a uniform photometric sample of 59 Galactic globular clusters that were observed by HST WFC/ACS as a part of the Globular Cluster Treasury project. Methods: We measured the fraction of binaries and the distribution of mass-ratio as a function of radial location within the cluster, from the central core to beyond the half-mass radius. We studied the radial distribution of binary stars, and the distribution of stellar mass ratios. We investigated monovariate relations between the fraction of binaries and the main parameters of their host clusters. Results: We found that in nearly all the clusters, the total fraction of binaries is significantly smaller than the fraction of binaries in the field, with a few exceptions only. Binary stars are significantly more centrally concentrated than single MS stars in most of the clusters studied in this paper. The distribution of the mass ratio is generally flat (for mass-ratio parameter q > 0.5). We found a significant anti-correlation between the binary fraction in a cluster and its absolute luminosity (mass). Some, less significant correlation with the collisional parameter, the central stellar density, and the central velocity dispersion are present. There is no statistically significant relation between the binary fraction and other cluster parameters. We confirm the correlation between the binary fraction and the fraction of blue stragglers in the cluster. Tables 1-3 and Appendices are only available in electronic form at http://www.aanda.org