Microwave rotational transitions have been observed at low J (0-3) for several isotopic species of the Ne-HCN dimer using the Balle/Flygare Mark II Fourier transform spectrometer with a pulsed nozzle as the source. For Ne-20-(HCN)-N-14, the main K=0 transitions give rotational constants BBAR, D(J), and H(J) of 2772.816 and 1.280 MHz and 1. 173 kHz. The N-14 nuclear quadrupole constant increases linearly with J(J + 1) at a slope D(chi) of - 12.7 kHz from a value for chi(a)(N-14) of -0.957 MHz at J=0. The pseudodiatomic approximation for BBAR and chi(a)(N-14) leads to a value of 3.89 angstrom for the Ne to (HCN)-N-14 center-of-mass (c.m.) distance R, and to 46.8-degrees for the ''average'' bend angle theta of (HCN)-N-14. Some of the K=0, J=1 --> 2, and J=2 --> 3 transitions exhibit one or two weak satellites approximately 30 MHz away, usually below, but also both above and below. The J=1 --> 2 low frequency satellites for Ne-20-(HCN)-N-14 and Ne-20-(HCN)-N-15, nominally 1(11) --> 2(1)2, are symmetrical doublets with splittings of 305 and 439 kHz, respectively. The N-14 hyperfine structure (hfs) is identical for the two Ne-20-(HCN)-N-14 components as is the Stark effect for Ne-20-(HCN)-N-15. The molecular mechanics for clusters (MMC) model was used to calculate potential energy surfaces for Rg-HCN dimers, giving stabilities of 21, 37, 85, and 108 cm-1 with He, Ne, Ar, and Kr as the rare gas. A qualitative comparison of the experimental properties for the dimers with Ne, Ar, and Kr as the rare gas is based on the surfaces. The extremely mobile internal dynamics of Ne-HCN are attributed to its potential surface, which is both very shallow and isotropic.