To study the effects of hydrocarbon precursor gases, graphene is grown by chemical vapor deposition from methane, ethane, and propane on copper foils. The larger molecules are found to more readily produce bilayer and multilayer graphene, due to a higher carbon concentration and different decomposition processes. Single- and bilayer graphene can be grown with good selectivity in a simple, single-precursor process by varying the pressure of ethane from 250 to 1000 mTorr. The bilayer graphene is AB-stacked as shown by selected area electron diffraction analysis. Additionally propane is found to only produce a combination of single- to few-layer and turbostratic graphene. The percent coverage is investgated using Raman spectroscopy and optical, scanning electron, and transmission electron microscopies. The data are used to discuss a possible mechanism for the second-layer growth of graphene involving the different cracking pathways of the hydrocarbons.