Epigenetic regulation involves changes in gene expression independent of DNA sequence variation that are inherited through cell division. In addition to a fundamental role in cell differentiation, some epigenetic changes can also be transmitted transgenerationally through meiosis. Epigenetic alterations (epimutations) could thus contribute to heritable variation within populations and be subject to evolutionary processes such as natural selection and drift. However, the rate at which epimutations arise and their typical persistence are unknown, making it difficult to evaluate their potential for evolutionary adaptation. Here, we perform a genome-wide study of epimutations in a metazoan organism. We use experimental evolution to characterize the rate, spectrum and stability of epimutations driven by small silencing RNAs in the model nematode Caenorhabditis elegans. We show that epimutations arise spontaneously at a rate approximately 25 times greater than DNA sequence changes and typically have short half-lives of two to three generations. Nevertheless, some epimutations last at least ten generations. Epimutations mediated by small RNAs may thus contribute to evolutionary processes over a short timescale but are unlikely to bring about long-term divergence in the absence of selection.