In conventional Kerr-and Faraday microscopy the sample is illuminated with plane-polarised light and a magnetic domain contrast is generated by an analyser making use of the Kerr-or Faraday rotation. In this paper we demonstrate possibilities of analyser-free magneto-optical microscopy based on magnetisationdependent intensity modulations of the light: (i) The transverse Kerr effect can be applied for in-plane magnetised material, demonstrated for an FeSi sheet. (ii) Illuminating the same sample with circularly polarised light leads to a domain contrast with a different symmetry as the conventional Kerr contrast. (iii) Circular polarisation can also be used for perpendicularly magnetised material, demonstrated for a garnet film and an ultrathin CoFeB film. (iv) Plane-polarised light at a specific angle can be employed for both, in-plane and perpendicular media. (v) Perpendicular light incidence leads to a domain contrast on in-plane materials that is quadratic in the magnetisation and to a domain boundary contrast. (vi) Domain contrast can even be obtained without polariser. In cases (ii) and (iii), the contrasts are generated by MCD (Magnetic Circular Dichroism), i.e. by the differential absorption of left and right circularly polarised light, induced by magnetization components along the direction of light propagation. In case (v) the contrast is caused by MLD (Magnetic Linear Dichroism), i.e. by the differential absorption of linearly polarised light, induced by magnetisation components transverse to the propagation direction. The domain boundary contrast is due to the magneto-optical gradient effect. An explanation of these contrast phenomena is provided in terms of Maxwell-Fresnel theory.