The magnetic fields of the Earth and other planets deviate in varying degrees from symmetry about the rotational axis. While, for example, the field of Saturn is highly symmetric, that of Uranus shows a striking asymmetry. With these observations in mind we investigate excitation conditions of axisymmetric and non-axisymmetric field modes in spherical mean-field dynamo models. In models of α2-type the marginal dynamo numbers for modes with different azimuthal dependences are close together if the α-effect is concentrated in a thin layer. Preference of non-axisymmetric modes over axisymmetric ones occurs if we include weak differential rotation, anisotropies of the α-effect or the γ-effect, the last one corresponding to a radial transport of magnetic flux. We discuss consequences of these results for planetary dynamos.