Artificial neural networks are parallel computational algorithms which can simulate very efficiently complex dynamical systems. In this work we show, by means of real-world applications, that this technique can be a useful tool in the analysis of time-series data related to climate. We study two time series: the first one characterizes the solar activity as measured by the annual mean value of the sunspot number (Wolf number); the second one is the record of summer monsoon rainfall over India. Both records are often used in the literature as benchmarks for testing new statistical techniques. From these studies we conclude that artificial neural networks can advantageously substitute conventional methods of time series analysis. Moreover, they reveal themselves as a promising way of making predictions on climatic phenomena.