We consider the problem of distributed delivery of correlated data from sensors in ad hoc network topologies. We propose to use network coding in order to exploit the path diversity in the network for efficient delivery of the sensor information. We further show that the correlation between the data sources can be exploited at receivers for efficient approximate decoding when the number of received data packets is not sufficient for perfect decoding. We analyze how the decoding performance is influenced by the choice of the network coding parameters and in particular by the size of finite fields. We determine the optimal field size that maximizes the expected decoding performance, which actually represents a trade-off between information loss incurred by quantizing the source data and the error probability in the reconstructed data. Moreover, we show that the decoding performance improves when the accuracy of the correlation estimation increases. We have illustrated our network coding based algorithms with approximate decoding in sensor networks and video coding applications. In both cases, the experimental results confirm the validity of our analysis and demonstrate the benefits of our solution for distributed delivery of correlated information in ad hoc networks.