The electronic structures of known N-heterocyclic carbenes (NHCs) with boron, nitrogen, and phosphorus backbones are examined using quantum chemical methods and compared to the experimental results and to the computational data obtained for a classical carbon analogue, imidazol-2-ylidene. The sigma-donor and pi-acceptor abilities of the studied NHCs in selected transition-metal complexes are evaluated using a variety of approaches such as energy and charge decomposition analysis, as well as calculated acidity constants and carbonyl stretching frequencies. The study shows that the introduction of selected heteroatoms into the NHC backbone generally leads to stronger metal-carbene bonds and therefore improves the ligand properties of these systems. The backdonation of pi-electron density from the metal to the ligand is found to be strong in complexes of the studied NHCs with group 11 metals, where it constitutes up to nearly 35% of the total orbital interaction energy. The ligand properties of the aluminum analogues of some of the reported NHCs with boron backbones are also assessed.