Using the scaling theory of quantum critical phenomena we explore the occurrence of universal critical behavior at the insulator-to-superconductor and superconductor-to-normal state transitions at zero temperature. Experimentally, these phase transitions are driven by doping and correspond to critical end points of the phase transition łine in the temperature-hole concentration plane. Provided that the order parameter is a complex scalar in two dimensions, and that the London relation between superfluid number density and magnetic penetration depth holds, the scaling theory predicts universal behavior close to the insulator-to-superconductor transition. In particular, transition temperature and zero temperature penetration depth are universally related and the sheet resistance adopts a universal value. These predictions agree remarkably well with available experimental data and provide useful constraints for a microscopic theory.PACS numbers: 74.62.Dh Many physical properties of cuprate superconductors depend on hole doping. The generic doping dependence of the transition temperature Tc is depicted in Fig. 1. At a certain doping level, the so-called underdoped limit, these materials undergo at the hole concentration x" and T > O a transition from insulator to anomalous metal, and at T = O a transition from insulator to superconductor. As x is increased, Tc rises and reaches its maximum at x m . This behavior is shared by many cuprates, . In some compounds a further increase in the doping level leads to more metallic normal-state properties [8,9], but T, decreases and vanishes in the overdoped limit xo. Here, these materials undergo at T = O a superconductor-to-normal-state transition. A prominent example is La2_x S rx C uO4 _ δ [2].Another essential and doping-dependent property is the effective mass an-