The low-lying electronic states of NbCn with five different geometries, namely, ring (R), linear (L), kite (K), Nb-terminally bound to a C-n ring (T), and a structure with C-Nb-C bridge fused with a C-n ring (A) (n > 3) are considered for n = 3-8. Three different levels of theoretical techniques, viz., complete active space multiconfiguration self-consistent field, multireference singles + doubles configuration interaction, and density functional theory were considered. We compute the equilibrium geometries, energy separations of the low-lying electronic states, Gibbs free energies, and heat capacity functions as a function of temperatures. For smaller clusters such as NbC3, NbC4, and NbC5, we find the ring structure to be lower with the linear structure as the first excited structure. Larger clusters exhibit odd-even alternation in that for even n the linear and ring structures are very close, whereas the clusters with odd n exhibit lower ring structures analogous to the smaller clusters. NbC6 was found to be unusual in having a linear ground state.