We report the synthesis of cobalt nanoparticles with different shapes and sizes by rapid pyrolysis of cobalt carbonyl in the presence of various surfactants. The size and shape of the nanoparticles were influenced by reaction conditions, such as type of the surfactant, molar ratio of surfactant to precursor, reflux temperature and reaction time. The shapes that we have achieved include spherical, nearly spherical, disc and cube. The presence of linear amine yielded nanodiscs and they spontaneously self-assembled into long ribbons. The effect of shape anisotropy on magnetic nanoparticles has been investigated. Spherical nanoparticles of diameter 14.5 nm show strong ferromagnetic behavior at low temperature and superparamagnetism at room temperature. On the other hand the cubic nanoparticles of 45 nm sides showed negligible coercive field at T=10 K and ferromagnetism that persisted above T=300 K. The cobalt nanospheres were oxidized to grow cobalt oxide shell of varying thickness to study exchange bias effect. A pronounced exchange bias and a strong temperature dependant magnetization were observed in oxidized cobalt nanospheres.