Protonic conductivity in the KH2PO4 family of hydrogen-bonded insulators has been studied via the proton NMR lineshape and the decay of the NMR transverse nuclear spin magnetization of Rb-87 nuclei in a spatially inhomogeneous electric field gradient. A large difference in the time scales of the decays of Hahn spin echo and Carr-Purcell echo train was observed. The Hahn echo decay curves show an exponential decay with the exponent proportional to the cube of time that is characteristic for diffusive motions. The proton NMR spectrum demonstrates the presence of mobile protons which produce a motionally narrowed absorption line above 220 K. The same effects were observed in several pure ferroelectric and antiferroelectric members of the KH2PO4 family as well as in their mixtures - the proton glasses.