Modified bases in nucleic acids present a layer of information that directs biological function over and beyond the coding capacity of the conventional bases. While a large number of modified bases have been identified, many of the enzymes generating them still remain to be discovered. Recently, members of the 2-oxoglutarate- and iron(II)-dependent dioxygenase superfamily, which modify diverse substrates from small molecules to biopolymers, were predicted and subsequently confirmed to catalyze oxidative modification of bases in nucleic acids. Of these, two distinct families, namely the AlkB and the kinetoplastid base J binding proteins (JBP) catalyze in situ hydroxylation of bases in nucleic acids. Using sensitive computational analysis of sequences, structures and contextual information from genomic structure and protein domain architectures, we report five distinct families of 2-oxoglutarate- and iron(II)-dependent dioxygenase that we predict to be involved in nucleic acid modifications. Among the DNA-modifying families, we show that the dioxygenase domains of the kinetoplastid base J-binding proteins belong to a larger family that includes the Tet proteins, prototyped by the human oncogene Tet1, and proteins from basidiomycete fungi, chlorophyte algae, heterolobosean amoeboflagellates and bacteriophages. We present evidence that some of these proteins are likely to be involved in oxidative modification of the 5-methyl group of cytosine leading to the formation of 5-hydroxymethylcytosine. The Tet/JBP homologs from basidiomycete fungi such as Laccaria and Coprinopsis show large lineage-specific expansions and a tight linkage with genes encoding a novel and distinct family of predicted transposases, and a member of the Maelstrom-like HMG family. We propose that these fungal members are part of a mobile transposon. To the best of our knowledge, this is the first report of a eukaryotic transposable element that encodes its own DNA-modification enzyme with a potential regulatory role. Through a wider analysis of other poorly characterized DNA-modifying enzymes we also show that the phage Mu Mom-like proteins, which catalyze the N6-carbamoylmethylation of adenines, are also linked to diverse families of bacterial transposases, suggesting that DNA modification by transposable elements might have a more general presence than previously appreciated. Among the other families of 2-oxoglutarate- and iron(II)-dependent dioxygenases identified in this study, one which is found in algae, is predicted to mainly comprise of RNA-modifying enzymes and shows a striking diversity in protein domain architectures suggesting the presence of RNA modifications with possibly unique adaptive roles.  The results presented here are likely to provide the means for future investigation of unexpected epigenetic modifications, such as hydroxymethyl cytosine, that could profoundly impact our understanding of gene regulation and processes such as DNA demethylation.