Dispersions of board-like goethite (a-FeOOH) particles with short-range repulsive interaction form a versatile colloidal model system, showing a nematic, smectic A and columnar phase. In high magnetic fields a biaxial nematic phase is induced with the shortest dimension of the particles aligned along the field. Moreover, if particles have a shape almost exactly in between rod-like and plate-like they can spontaneously, without external magnetic field, form biaxial nematic and biaxial smectic A phases, which is in accordance with theoretical predictions. The macroscopic domains were oriented by a magnetic field and their structure was revealed by small-angle X-ray scattering. Our results suggest that biaxial phases can be readily obtained by a proper choice of the particle shape.