*DNA methylation can cause heritable phenotypic modifications in the absence of changes in DNA sequence. Environmental stresses can trigger methylation changes and this may have evolutionary consequences, even in the absence of sequence variation. However, it remains largely unknown to what extent environmentally induced methylation changes are transmitted to offspring, and whether observed methylation variation is truly independent or a downstream consequence of genetic variation between individuals. *Genetically identical apomictic dandelion (Taraxacum officinale) plants were exposed to different ecological stresses, and apomictic offspring were raised in a common unstressed environment. We used methylation-sensitive amplified fragment length polymorphism markers to screen genome-wide methylation alterations triggered by stress treatments and to assess the heritability of induced changes. *Various stresses, most notably chemical induction of herbivore and pathogen defenses, triggered considerable methylation variation throughout the genome. Many modifications were faithfully transmitted to offspring. Stresses caused some epigenetic divergence between treatment and controls, but also increased epigenetic variation among plants within treatments. *These results show the following. First, stress-induced methylation changes are common and are mostly heritable. Second, sequence-independent, autonomous methylation variation is readily generated. This highlights the potential of epigenetic inheritance to play an independent role in evolutionary processes, which is superimposed on the system of genetic inheritance.