It turns out, there are a few viruses with nearly ubiquitous presence in the population that are probably living in your brain right now...
Cytomegalovirus : This one is a favorite. It infects 80% of the population, but usually causes no symptoms. Its known to be latent in a couple types of immune cells, but it may hide elsewhere. Its spread in saliva, so can be transmitted by something as benign as sharing silverware or kissing. As a herpesvirus, it has several tricks for evading the immune system and is a persistent life-long infection. In some individuals, the infection can lead to a syndrome that mimics multiple sclerosis, which (I speculate) may indicate that the virus is replicating in oligodendrocytes, (or just that one antibody against CMV accidentally also recognizes a protein in myelin). This one can also turn lethal in immunosuppressed patients. And, best of all, it probably causes one of the most deadly forms of brain cancer.
Varicella Zoster ( chicken-pox ) : (90%) When I was growing up, it was common for parents to deliberately expose their kids to chicken pox in order to catch this virus in a stage of development where it is least deadly. I kind of hate my parents for this since, if they had just waited, I could of had the vaccine rather than having the lovely little viral DNA in my brain-stem waiting to cause shingles. Fun.
JC virus : 70-90% of the population are carriers. It appears to reproduce primarily using your kidneys, but you'll hardly notice. Its related to BK virus, but that one doesn't eat your brain. SV40 may act similarly. It will eventually come to live in your astrocytes ( support cells in the brain ) and oligodendrocytes ( insulating cells in your brain ). You'll be fine ... unless you get AIDS, have an organ transplant, or need immunosuppression -- then the virus will kill your oligodendrocytes, (killing you). This one spreads readily via sewage (it's shed in urine).
Epstein-Barr virus (Mononucleosis "Mono") : Well known for being spread by kissing, something like 95% of adults in the US have this virus latent in their body. It seems like current research suggests that this herpesvirus lies dormant in B cells, not neurons, but the acute phase of the infection can have neurological complications. It can eventually cause cancers, but I can't find any info on chronic neurological effects at the moment. It might be a cause of some cases of multiple sclerosis.
HSV [1/2]: This is what most of us know simply as "herpes". This one will lie dormant in your brain stem or spinal column, and (might.. might) cause Bell's palsy or contribute to Alzheimer's. If I understand correctly (that is, if I am to believe 7th grade health class and wikipedia), HSV1 is ubiquitous (80%) and you usually pick it up from your parents when you're a kid, while HSV2 is the sexually transmitted variant. So, you probably have HSV1 living in your brain at the moment, and depending on your lifestyle, may or may not have HSV-2 ( apparently often asymptomatic ) there as well.
Honorable mentions :
Measles can remain latent for years in the nervous system, eventually causing Subacute sclerosing panencephalitis, which can kill you over the course of 3 years, with progressive mental deterioration. A similar rare condition can occur with rubella. HIV and prion disease also deserve honorable mentions. Hopefully you know if you have HIV, and prion disease is extremely rare. Polio is still out there and chronic fatigue syndrome might be caused by XMRV. Human T-lymphotropic virus 1 is rare but will cause a chronic neurological disorder. Then, of course, we have the numerous viruses that can cause encephalitis and meningitis. The way Rabies destroys the brain would actually be really cool if it weren't so terrible.
Well, this has been fun, but it turns out that there are even more interesting slow viruses living in some of your other tissues, just waiting to cause a fatal cancer or bring you down should your immune system falter. This makes me wonder how many unexplained diseases may be caused by as yet uncharacterized viruses.
To get a start on some of the other fun and terrifying viruses, see :