The nature and the universal properties of DNA thermal denaturation are investigated by Monte Carlo simulations. For suitable lattice models we determine the exponent c describing the decay of the probability distribution of denaturated loops of length l, P approximately l(-c). If excluded volume effects are fully taken into account, c = 2.10(4) is consistent with a first order transition. The stiffness of the double stranded chain has the effect of sharpening the transition, if it is continuous, but not of changing its order and the value of the exponent c, which is also robust with respect to inclusion of specific base-pair sequence heterogeneities.