Birds have the smallest genomes among land vertebrates. Their genome sizes are roughly a third of the human genome due to massive genome compaction in their dinosaur ancestors, potentially resulting from the metabolic requirements of powered flight. Consequently, transposable elements are relatively scarce in avian genomes and it has been suggested that rarity of transposition explains the stability of genome size and chromosomal organization across extant birds. Here we show that avian genomes instead have a dynamic and diverse landscape of transposition-derived structural variation. We analyzed 201 re-sequenced genomes of six species of Ficedula flycatchers and a three-generation pedigree of eleven collared flycatchers for transposable element variation (TEV). Following read mapping and stringent filtering, we discovered >10,000 transposon presence/absence polymorphisms. These TEVs include many which are shared between multiple species, however, around two thirds of the TEVs are private alleles. In combination with our pedigree data, this suggests that transposition occurs relatively frequently in flycatchers. Most TEVs belong to eight different families of long terminal repeat (LTR) retrotransposons from the major groups of endogenous retroviruses (ERV); ERV1, ERV2, and ERV3. We further find that chromosomal recombination rate and density of sites under selection are predictors of TEV abundance. Altogether, we suggest that transposition is relatively frequent and diverse in birds, and that the overall scarcity of fixed transposable elements in avian genomes results from rare retention of TEVs due to low population frequencies.