Orthopoxviruses and some other nucleocytoplasmic large DNA viruses synthesize RNA using a virally encoded multi-subunit RNAP. They are most similar to eukaryotic RNAPs, with some subunits minified or removed. Exactly which RNAP they are most similar to is a topic of debate. Most other viruses that synthesize RNA use unrelated mechanics.
Many viruses use a single-subunit DNA-dependent RNAP (ssRNAP) that is structurally and mechanistically related to the single-subunit RNAP of eukaryotic chloroplasts (RpoT) and mitochondria (POLRMT) and, more distantly, to DNA polymerases and reverse transcriptases. Perhaps the most widely studied such single-subunit RNAP is bacteriophage T7 RNA polymerase. ssRNAPs cannot proofread.
B. subtilis prophage SPβ uses YonO, a homolog of the β+β′ subunits of msRNAPs to form a monomeric (both barrels on the same chain) RNAP distinct from the usual "right hand" ssRNAP. It probably diverged very long ago from the canonical five-unit msRNAP, before the time of the last universal common ancestor.
Other viruses use an RNA-dependent RNAP (an RNAP that employs RNA as a template instead of DNA). This occurs in negative strand RNA viruses and dsRNA viruses, both of which exist for a portion of their life cycle as double-stranded RNA.  However, some positive strand RNA viruses, such as poliovirus, also contain RNA-dependent RNAP.