H-1 nuclear magnetic resonance (NMR) field cycling relaxometry has been applied to study the dynamics of homologues of glycerol (propylene glycol, 2,3-butandiol, glycerol, threitol, xylitol, sorbitol) and non-alcohol liquids (o-terphenyl, tristyrene, 3-fluoroaniline, in-toluidine). A broad range of temperatures (200-400 K) is covered, including the supercooled state. From the dispersion of the spin-lattice relaxation rate, R-1(omega) = T-1(-1)(omega), the susceptibility representation, omega T-1(-1)(omega), has been derived and compared with the susceptibility data from dielectric spectroscopy (DS). The DS spectra can be interpolated by a Cole-Davidson (CD) function, yielding correlation times which are attributed to the structural relaxation (alpha-process) in the supercooled state. In contrast to that, most or the H-1 NMR susceptibility spectra show, in addition to the alpha-relaxation peak, a low-frequency excess contribution with amplitudes varying among the systems. Exceptions are o-terphenyl and tristyrene for which DS and NMR susceptibility curves agree well and both can be reproduced by a CD function. Possible explanations of the low-frequency contribution are discussed. In particular the role of translational diffusion probed via the intermolecular coupling of H-1 spins is considered since it may likely generate the low-frequency excess intensity.