We experimentally study the formation of cusps at the free surfaces of viscous fluids in three simple cases that portray possible natural or industrial processes. Two cases concern levelling driven by gravity: the case (A) of a sinusoidal surface and the case (B) of a single groove. In the third case (C), an initially sinusoidal surface evolves under the action of a fast enough lateral compression that the effects of gravity are negligible. Case (A) shows a critical aspect ratio above which the cusps form. Case (B) allows a more detailed study of the evolution of the cuspidal structure, which does not change in shape but reduces its size according to a simple power law dependence in time. In case (C), cusps form even for small initial aspect ratios.