In this paper the influence of stationary magnetic fields of arbitrary direction on three-dimensional natural convection in liquid metals is investigated. The liquid metal is confined in electrically insulating rectangular cavities. The convection is driven by horizontal or vertical temperature gradients. A second-order finite-difference method is employed to solve the basic dimensionless equations. Electric current paths and the effect of resulting Lorentz forces on the organisation of flow and heat transport are studied. Electric currents often close within the fluid without short circuiting through Hartmann layers. Typical flow patterns show excessive intensities in regions close to corners.