We experimentally investigate electrical transport properties of graphene, which is a two dimensional (2D) conductor with relativistic energy dispersion relation. By investigating single- and bi-layer graphene devices with different aspect ratios, we confirm experimentally that the minimum conductivity in wide and short graphene strips approaches the theoretical value of 4e^2/\pi\h. At low temperatures, quantum interference of multiply-reflected waves of electrons and holes in graphene give rise to periodic conductance oscillations with bias and gate voltages. Thus graphene acts as a quantum billiard, a 2D ballistic, phase coherent electron system with long phase coherence length that exceeds 5 microns. Additional features in differential conductance emerge when graphene is coupled to superconducting electrodes. We observe proximity-induced enhanced conductance at low bias, and conductance dips at energy scales far above the superconducting gap of the electrodes. The latter provides preliminary evidence for a novel superconducting material that consists of graphene coated with metallic atoms.