Sequencing errors and random sampling of nucleotide types among sequencing reads at heterozygous sites present challenges for accurate, unbiased inference of single-nucleotide polymorphism genotypes from high-throughput sequence data. Here, we develop a maximum-likelihood approach to estimate the frequency distribution of the number of alleles in a sample of individuals (the site frequency spectrum), using high-throughput sequence data. Our method assumes binomial sampling of nucleotide types in heterozygotes and random sequencing error. By simulations, we show that close to unbiased estimates of the site frequency spectrum can be obtained if the error rate per base read does not exceed the population nucleotide diversity. We also show that these estimates are reasonably robust if errors are nonrandom. We then apply the method to infer site frequency spectra for zerofold degenerate, fourfold degenerate, and intronic sites of protein-coding genes using the low coverage human sequence data produced by the 1000 Genomes Project phase-one pilot. By fitting a model to the inferred site frequency spectra that estimates parameters of the distribution of fitness effects of new mutations, we find evidence for significant natural selection operating on fourfold sites. We also find that a model with variable effects of mutations at synonymous sites fits the data significantly better than a model with equal mutational effects. Under the variable effects model, we infer that 11% of synonymous mutations are subject to strong purifying selection.