The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport also supercurrent transport has already been observed. It has also been suggested that graphene might be a promising material for spintronics and related applications, such as the realization of spin qubits, due to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. As a first step in the direction of graphene spintronics and spin qubits we report the observation of spin transport, as well as Larmor spin precession over micrometer long distances using single graphene layer based field effect transistors. The non-local spin valve geometry was used, employing four terminal contact geometries with ferromagnetic cobalt electrodes, which make contact to the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals which reflect the magnetization direction of all 4 electrodes, indicating that spin coherence extends underneath all 4 contacts. No significant changes in the spin signals occur between 4.2K, 77K and room temperature. From Hanle type spin precession measurements we extract a spin relaxation length between 1.5 and 2 micron at room temperature, only weakly dependent on charge density, which is varied from n~0 at the Dirac neutrality point to n = 3.6 10^16/m^2. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around 10%.