We have fabricated graphene-silicon Schottky diodes by depositing mechanically exfoliated graphene on top of silicon substrates. The resulting current-voltage characteristics exhibit rectifying diode behavior with a barrier energy of 0.41 eV on n-type silicon and 0.45 eV on p-type silicon at the room temperature. The I-V characteristics measured at 100, 300, and 400 K indicate that temperature strongly influences the ideality factor of graphene-silicon Schottky diodes. The ideality factor, however, does not depend strongly on the number of graphene layers. The optical transparency of the thin graphene layer allows the underlying silicon substrate to absorb incident laser light and generate a photocurrent. Spatially resolved photocurrent measurements reveal the importance of inhomogeneity and series resistance in the devices.