We measured the mobility of excess electrons in the polar hydrogen cyanide gas (D = 2.985 D) at low densities as a function of density and temperature by the so-called pulsed Townsend method. Experiments were performed at 294 and 333 K in the gas number density range 1.23x10(17)less than or equal to n less than or equal to 3.61x10(18) cm(-3). We found a strong density dependence of the ''zero-field'' density-normalized mobility (mu n). Only about 10% of the observed density variation can be qualitatively explained by coherent and incoherent multiple scattering effects. With increasing gas density an increasing number of linear HCN dimers is formed which due to the high dipole moment (D=6.552 D) represent much stronger electron scatterers than the HCN monomers. It was found that the dimers may be only in part responsible for the observed density effect. Therefore, we consider a transport process where short-lived dipole-bound electron ground states (lifetime greater than or equal to 12 ps) as quasilocalized states are involved. For comparison the electron mobility in saturated 2-aminoethanol vapor with a dipole moment of similar size (D = 3.05 D) does not show any anomalous density behavior in the temperature range 298 less than or equal to T less than or equal to 435 K. In contrast to this the electron mobility in saturated but also in nonsaturated CH3CN gas (D = 3.925 D) shows a density behavior similar to that in HCN.