The neutral hydrogen properties of 1822 galaxies are being studied with the Green Bank 100-m and the Parkes 64-m telescopes as part of the ‘Cosmic Flows’ programme. Observed parameters include systemic velocities, profile linewidths and integrated fluxes. The linewidth information can be combined with the optical and infrared photometry to obtain distances. The 1822 H i observations complement an inventory of archives. All told, H i linewidth information is available for almost all of five samples: (i) luminosity–linewidth correlation calibrators; (ii) zero-point calibrators for the Type Ia supernova scale; (iii) a dense local sample of spiral galaxies with within 3000 km s−1; (iv) a sparser sample of 60-μm selected galaxies within 6000 km s−1 that provides an all-sky coverage of our extended supercluster complex; and (v) an even sparser sample of flat galaxies, extreme edge-on spirals, extending in a volume out to 12 000 km s−1. The H i information for 13 941 galaxies, whether from the archives or acquired as part of the Cosmic Flows observational programme, is uniformly re-measured and made available through the Extragalactic Distance Database website.