We discuss and compare the multifractal temporal scaling properties of precipitation and river discharge records on large timescales. To detect long-term correlations and multifractal behavior in the presence of trends, we apply recently developed methods (detrended fluctuation analysis (DFA) and multifractal DFA) that can systematically detect nonstationarities and overcome trends in the data at all timescales. We find that above some crossover time that usually is several weeks, the daily runoffs are characterized by an asymptotic scaling exponent that indicates a slow power law decay of the runoff autocorrelation function and varies from river to river in a wide range. Below the crossovers, pronounced short-term correlations occur. In contrast, most of the precipitation series show scaling behavior corresponding to a rapid decay of the autocorrelation function. For the multifractal characterization of the data we determine the generalized Hurst exponents and fit them by three operational models. While the fits based on the universal multifractal model describe well the scaling behavior of the positive moments in nearly all runoff and precipitation records, positive as well as negative moments are consistent with two-parameter fits from a modified version of the multiplicative cascade model for all runoff records and most of the precipitation records. For some precipitation records with weak multifractality, however, a simple bifractal characterization gives the best fit of the data.