We present results of a study of neutral hydrogen (HI) in a complete sample of nearby non-cluster radio galaxies. We find that radio galaxies with large amounts of extended HI (M_HI >= 10^9 M_solar) all have a compact radio source. The host galaxies of the more extended radio sources, all of Fanaroff & Riley type-I, do not contain these amounts of HI. We discuss several possible explanations for this segregation. The large-scale HI is mainly distributed in disk- and ring-like structures with sizes up to 190 kpc and masses up to 2 x 10^10 M_solar. The formation of these structures could be related to past merger events, although in some cases it may also be consistent with a cold-accretion scenario.