We present the largest, most homogeneous catalogue of merging galaxies in the nearby Universe obtained through the Galaxy Zoo project – an interface on the World Wide Web enabling large-scale morphological classification of galaxies through visual inspection of images from the Sloan Digital Sky Survey (SDSS). The method converts a set of visually inspected classifications for each galaxy into a single parameter (the ‘weighted-merger-vote fraction,’fm) which describes our confidence that the system is part of an ongoing merger. We describe how fm is used to create a catalogue of 3003 visually selected pairs of merging galaxies from the SDSS in the redshift range 0.005 < z < 0.1. We use our merger sample and values of fm applied to the SDSS Main Galaxy Spectral sample to estimate that the fraction of volume-limited (Mr < −20.55) major mergers (1/3 < M*1/M*2 < 3) in the nearby Universe is 1–3 ×C per cent, where C∼ 1.5 is a correction factor for spectroscopic incompleteness. Having visually classified the morphologies of the constituent galaxies in our mergers, we find that the spiral-to-elliptical ratio of galaxies in mergers is higher by a factor of ∼2 relative to the global population. In a companion paper, we examine the internal properties of these merging galaxies and conclude that this high spiral-to-elliptical ratio in mergers is due to a longer time-scale over which mergers with spirals are detectable compared to mergers with ellipticals.