Well, I understood dna to mean genetic basis in the context of this discussion, but yes. There are in fact RNA and DNA Viruses, which can further be divided in coding and non-coding strand (+ and -) based "liveforms".

There are also Prions, proteins that fold others with the same base aminoacid-chain into the same 3D struckture, in a kind of replication.

Viroids are naked, or non protein or membrane, associated chains of RNA, able to infect plants and responsible for some interesting patterns on some flowers.

To complete the picture there are also gigant virus out there, with their own molecular maschinery responsible for about halve of our atmospheric O2.

These are complex little suckers. And I both love them for it and hate them with a passion.