Carbon-doped GaN was grown by plasma-assisted molecular-beam epitaxy using carbon tetrachloride vapor as the dopant source. For moderate doping mainly acceptors were formed, yielding semi-insulating GaN. However at higher concentrations p-type conductivity was not observed, and heavily doped films (>5x10^20 cm-3) were actually n-type rather than semi-insulating. Photoluminescence measurements showed two broad luminescence bands centered at 2.2 and 2.9 eV. The intensity of both bands increased with carbon content, but the 2.2 eV band dominated in n-type samples. Intense, narrow (~;6 meV) donor-bound exciton peaks were observed in the semi-insulating samples.