Determining the amount of recombination in the genealogical history of a sample of genes is important to both evolutionary biology and medical population genetics. However, recurrent mutation can produce patterns of genetic diversity similar to those generated by recombination and can bias estimates of the population recombination rate. Hudson 2001 has suggested an approximate-likelihood method based on coalescent theory to estimate the population recombination rate, 4N(e)r, under an infinite-sites model of sequence evolution. Here we extend the method to the estimation of the recombination rate in genomes, such as those of many viruses and bacteria, where the rate of recurrent mutation is high. In addition, we develop a powerful permutation-based method for detecting recombination that is both more powerful than other permutation-based methods and robust to misspecification of the model of sequence evolution. We apply the method to sequence data from viruses, bacteria, and human mitochondrial DNA. The extremely high level of recombination detected in both HIV1 and HIV2 sequences demonstrates that recombination cannot be ignored in the analysis of viral population genetic data.