We investigated the fluctuations (noise) in the positions and friction forces of rectangular blocks, made from rubber or polymethyl methacrylate (PMMA), sliding on various substrates under constant driving forces. The experimental results are compared to simulations and analytical results using simple models for the interaction between the solids at the sliding interface. In particular, we use spring-block and asperity-force models, and an analytical wear-particle model. In the spring-block model, small (mini) blocks, representing the asperity contact regions, are connected by viscoelastic springs to a larger block. The miniblocks interact with the substrate with forces that fluctuate randomly in time and magnitude. The wear particle model considers the irregular motion of different-sized wear particles at the interface. The spring-block and wear-particle models predict displacement and force power spectra which, in wide frequency regions, are power-laws, with exponents in agreement with the experiments. The asperity-force model assumes a sliding block with a smooth surface and a randomly rough substrate. In this case the force on the big block results from fluctuations in the number and the size of asperity contact regions. This model gives power spectra that disagree with experimental observations.