Cells use complex networks of interacting molecular components to transfer and process information. These "computational devices of living cells" are responsible for many important cellular processes, including cell-cycle regulation and signal transduction. Here we address the issue of the sensitivity of the networks to variations in their biochemical parameters. We propose a mechanism for robust adaptation in simple signal transduction networks. We show that this mechanism applies in particular to bacterial chemotaxis. This is demonstrated within a quantitative model which explains, in a unified way, many aspects of chemotaxis, including proper responses to chemical gradients. The adaptation property is a consequence of the network's connectivity and does not require the 'fine-tuning' of parameters. We argue that the key properties of biochemical networks should be robust in order to ensure their proper functioning.