Variation in the presence or absence of transposable element (TE) insertions in eukaryotic genomes is a significant source of genetic variation between individuals. Here, we identified 23,095 TE presence/absence variants between 216 wild Arabidopsis accessions. TE variants were identified that were associated with altered expression of nearby genes, indicating a possible functional role in the evolution of gene regulation. A majority of previously identified regions of differential DNA methylation between these accessions were associated with nearby TE variants, indicating an important role in facilitating epigenomic variation. Most TE variants are rare, however more than two thirds of the common alleles identified were not in linkage disequilibrium with nearby SNPs, revealing a potential rich source of missing heritability. An examination of TE regulation following intraspecific crosses between parents with differential TE content revealed that the absence of individual TEs from the paternal genome leads to DNA demethylation within maternal copies of these TEs in the embryo, reminiscent of Drosophila hybrid dysgenesis. This suggests that genetic differences between parents may lead to the formation of DNA methylation differences observed between individuals, and might enable activation of previously silent TEs.