We study the distribution of the nth energy level for two different one-dimensional random potentials. This distribution is shown to be related to the distribution of the distance between two consecutive nodes of the wavefunction. We first consider the case of a white noise potential and study the distributions of energy levels both in the positive and the negative part of the spectrum. It is demonstrated that, in the limit of a large system (L∞), the distribution of the nth energy level is given by a scaling law which is shown to be related to the extreme value statistics of a set of independent variables. In the second part we consider the case of a supersymmetric random Hamiltonian (potential V(x) = φ(x)² + φ'(x)). First we study the case where φ(x) is a white noise with zero mean. In particular, it is shown that the ground state energy, which behaves on average like exp (-L^1/3) in agreement with previous work, is not a self-averaging quantity in the limit L∞ as is seen in the case of diagonal disorder. Then we consider the case when φ(x) has a non-zero mean value.