We describe a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states. The probability can be computed at any temperature by weighting the density of states by the appropriate Boltzmann factor. Thermodynamic properties can be determined from suitable derivatives of the partition function and, unlike ''standard'' methods, the free energy and entropy can also be computed directly. To demonstrate the simplicity and power of the algorithm, we apply it to models exhibiting first-order or second-order phase transitions.