Diabetes Type I tends to occur in people that contain a certain blood virus (often they're born with it.) The next time you donate blood, look at your donor card. It'll relate your viral status just like it does your blood type. Apparently, they've discovered that children tend to develop diabetes if they're transfused with blood that contains the virus. (Sorry I can't remember its name. I just know because I asked about my status last time I donated and what it meant, and they explained "Basically, we can use your blood safely with children.")
Keep in mind its not a direct correlation: You might have the virus, but not diabetes. Or vice versa.
And outside of humans, Feline Leukemia is transmitted from close contact (such as fighting or sexual activity).
Hopefully this research, and research like it, will lead to breakthrough that allow us to better target virii and protect ourselves from them. The goal here, aside from eliminating life-impacting diseases such as HIV, HPV, and Herpes, but also eliminating the "common cold".
Finally people will no longer be able to say, "They can put a man on the moon, but they can't cure the common cold...".
I believe (found a nature paper about) that a virus closely linked with diabetes is Coxsackie.
One of the issues with the common cold is that it mutates fairly quickly, IIRC and there are a lot of them. HPV does not (there is a vaccine for some strains).
HPV (human papillomavirus) is a virus, not a cancer. Most people carry the virus but are asymptomatic. Of the approx 130 types of HPV, some can lead to cancer, most commonly of the cervix.