Thermally induced chemical vapor deposition (CVD) was used to study the formation of nitrogen-doped graphene and carbon films on copper from aliphatic nitrogen-containing precursors consisting of C1- and C2-units and (hetero)aromatic nitrogen-containing ring systems. The structure and quality of the resulting films were correlated to the influence of the functional groups of the precursor molecules and gas phase composition. They were analyzed with SEM, TEM, EDX, XPS, and Raman spectroscopy. The presence of (N-doped) graphene was confirmed by the 2D mode of the Raman spectra. The isolated graphene films obtained from nitrogen-containing precursors reveal a high conductivity and transparency compared to standard graphene CVD samples. Precursors with amine functional groups (e.g., methylamine) can lead to a direct formation of graphene even without additional hydrogen present in the gas phase. This is not observed for, e.g., methane under comparable CVD conditions. Therefore, the intermediate gas phase species (e.g., amine radicals) can significantly enhance the graphene film growth kinetics. Kinetic and thermodynamic effects can be invoked to discuss the decay of the precursors.