We studied the tunneling magnetoresistance (TMR) effect through a vacuum barrier using spin-polarized scanning tunneling microscopy on Co(0 0 0 1). By varying the gap width at a fixed bias voltage or by varying the bias voltage at a fixed gap width, the fundamental behaviour of the TMR across the vacuum gap was investigated. At large gap widths the TMR is constant with the width in agreement with Jullières model. At gap widths below 4.5 Å, a decrease of the TMR was found which cannot be explained on the basis of this model. The decrease is correlated with a strong decrease of the local barrier height underneath the tip and is explained in the framework of Slonczewski's model. The TMR across the vacuum barrier does not show the characteristic drop with bias voltage usually found in planar tunneling junctions but is rather independent on the voltage in case of large gap widths. This is related to the tunneling of electrons predominantly perpendicular to the Co(0 0 0 1) surface and the particular band structure of Co. The voltage dependence, however, is more complex at small gap width due to the opening up of the emission cone of the tunneling electrons.