Typically, people call viruses some kind of organic compounds that cannot reproduce autonomously and which lower the fitness of their hosts. Even the word "virus" means "venom" in Latin.

But from the perspective of natural selection, one would expect those organic compounds that cannot reproduce autonomously, but which would increase the fitness of their hosts, to be more widespread. One can see an analogy with bacteria: people are more aware of harmful bacteria and even such words as "microbe" are perceived as somewhat harmful (among non-biologists for sure). But we know that an animal body contains many more useful bacteria than harmful ones, and animals have their own microflora, which are necessary for survival.

The same must be true for viruses: those viruses which were useful (or at least unharmful) to their hosts would be passed more easily to other organisms since their hosts would have a selective advantage.

So, do such beneficial for their direct hosts viruses exist? If so, what are they called? What are the examples?

Do they exist? Yes

What are they called? Marilyn Roossinck calls them viral mutualistic symbiotes. She has an excellent review here. 

What are some examples?

My personal favorite is GB-Virus C, or Hepatitis G, which appears to slow the progression of HIV using a number of different mechanisms:


  Box 1. Summary of the effects of GBV-C infection in HIV-positive individuals
  
  
  GBV-C infection downregulates HIV entry co-receptors CCR5 and CXCR4, and increases secretion of their ligands RANTES, MIP-1α, MIP-1β and SDF-1.
  In vitro GBV-C NS5A and E2 proteins inhibit X4- and R5-tropic HIV replication, and NS5A protein downregulates CD4 and CXCR4 gene expression.
  HIV-infected individuals positive for GBV-C E2 antibodies have survival benefit over HIV-infected individuals with neither GBV-C viremia nor E2 antibodies; in vitro GBV-C E2 antibodies immunoprecipitate HIV particles and inhibit X4- and R5-tropic HIV replication.
  GBV-C induces activation of interferon-related genes and pDCs.
  GBV-C promotes Th1 polarization and the NS5A protein contributes to this effect.
  GBV-C infection reduces surface expression of activation markers on T lymphocytes, suggesting its role in T cell activation signaling pathways.
  GBV-C protects the T cell from Fas-mediated apoptosis and as a result of its effect on immune activation may also play a role in protecting lymphocytes from activation-induced cell death.
  GBV-C viremia reduces IL-2-mediated T cell proliferation suggesting a significant interaction between GBV-C, IL-2 and IL-2 signaling pathways.
  


Endogenous retroviruses

As @mbrig recalls in the comments, there are a number of retroviruses that have inserted themselves into the germ line. Those are called endogenous retroviruses, and they interact with the host genome in a number of ways. Some are even translated:


  Proteins produced from ERV env genes have also been demonstrated to function as restriction factors against exogenous retroviral infection

