There is massive variation in intron numbers across eukaryotic genomes, yet the major drivers of intron content during evolution remain elusive. Rapid intron loss and gain in some lineages contrast with long-term evolutionary stasis in others. Episodic intron gain could be explained by recently discovered specialized transposons called Introners, but so far Introners are only known from a handful of species. Here, we performed a systematic search across 3,325 eukaryotic genomes and identified 27,563 Introner-derived introns in 175 genomes (5.2%). Species with Introners span remarkable phylogenetic diversity, from animals to basal protists, representing lineages whose last common ancestor dates to over 1.7 billion years ago. Aquatic organisms were 6.5 times more likely to contain Introners than terrestrial organisms. Introners exhibit mechanistic diversity but most are consistent with DNA transposition, indicating that Introners have evolved convergently hundreds of times from nonautonomous transposable elements. Transposable elements and aquatic taxa are associated with high rates of horizontal gene transfer, suggesting that this combination of factors may explain the punctuated and biased diversity of species containing Introners. More generally, our data suggest that Introners may explain the episodic nature of intron gain across the eukaryotic tree of life. These results illuminate the major source of ongoing intron creation in eukaryotic genomes.