We describe results from a scanning Hall probe microscope operating in a broad temperature range, 4-300 K. A submicron Hall probe manufactured in a GaAs/AlGaAs two-dimensional electron gas is scanned over the sample to measure the surface magnetic fields using conventional scanning tunneling microscopy positioning techniques, The magnetic field structure of the sample together with the topography can be obtained simultaneously, The technique is noninvasive with an extremely low self-field of < 10(-2) G and yields a quantitative measurement of the surface magnetic field in contrast to magnetic force microscopy. in addition the microscope has an outstanding magnetic field resolution (similar to 1.1 x 10(-3) G/Hz at 77 K) and high spatial resolution, similar to 0.85 mu m, Images of individual vortices in a high-T-c Y1Ba2Cu3O7-gamma thin film at low temperatures and magnetic domains in an Fe-garnet crystal at room temperature are presented.