We present results of an H I study of a complete sample of nearby radio galaxies. Our goal is to investigate whether merger or interaction events could be at the origin of the radio-AGN activity. Around five of our radio galaxies, hosted mainly by early-type galaxies, we detect extended H I in emission. In most cases this H I is distributed in large (up to 190 kpc) and massive (up to MHI ∼ 1010 M⊙) disk- or ring-like structures, that show fairly regular rotation around the host galaxy. This suggests that in these systems a major merger likely occurred, but at least several Gyr ago. For the H I-rich radio galaxy B2 0648+27 we confirm such a merger origin through the detection of a post-starburst stellar population that dominates the visible light throughout this system. The timescale of the current episode of radio-AGN activity in our H I-rich radio galaxies is several orders of magnitude smaller than the merger timescales. Therefore the radio-AGN activity either started late in the lifetime of the merger event, or is not directly related to the merger event at all. Another intriguing result is that the H I-rich (> 109 M⊙) radio galaxies in our sample all have compact radio sources, while none of the extended radio sources contain these amounts of extended H I. This strongly suggests that there is a relation between the size of the radio jet and the presence of large amounts of neutral gas associated with the host galaxy.