Few-layer graphene films with a controllable thickness were grown on a nickel surface by rapid thermal annealing (RTA) under vacuum. The instability of nickel films in air facilitates the spontaneous formation of ultrathin (<2-3 nm) carbon- and oxygen-containing compounds on a nickel surface; thus, the high-temperature annealing of the nickel samples without the introduction of intentional carbon-containing precursors results in the formation of graphene films. From annealing temperature and ambient studies during RTA, it was found that the evaporation of oxygen atoms from the surface is the dominant factor affecting the formation of graphene films. The thickness of the graphene layers is strongly dependent on the RTA temperature and time, and the resulting films have a limited thickness (<2 nm), even for an extended RTA time. The transferred films have a low sheet resistance of +/- 0.4 k Omega/sq, with similar to 94% +/- 2% optical transparency, making them useful for applications as flexible transparent conductors.