Here's one to start you off - rats spread Weil's Disease. http://www.nhsdirect.nhs.uk/articles/article.aspx?articleId=230

Worldwide, rats and mice spread over 35 diseases. Rodent-borne diseases are spread directly to humans through bite wounds, consuming food or water that is contaminated with rodent feces, coming in contact with surface water contaminated with rodent urine, or through breathing in germs that may be present in rodent urine or droppings that have been stirred into the air. Diseases spread directly by Rodents are: Hantavirus Hemorrhagic fever Lassa fever Leptospirosis Lymphocytic Chorio-meningitis Omsk hemorrhagic fever Plague Rat-Bite fever Salmonellosis South American Arenaviruses Tularemia __________________________________________ Diseases from rodents are also spread indirectly to humans by way of ticks, mites, and fleas that transmit the infection to humans after feeding on infected rodents. In some cases, the rodents are the reservoirs (carriers) of the diseases, while in other cases the ticks, mites, or fleas act as the disease reservoirs. Diseases they can transmit indirectly Babesiosis (ticks) California serogroup viruses (including LaCrosse encephalitis) Colorado tick fever Cutaneous leishmaniasis Human granulocytic anaplasmosis Lyme disease Murine typhus Omsk hemorrhagic fever Powassan encephalitis Scrub typhus Rickettsialpox Relapsing fever Rocky Mountain spotted fever Sylvatic typhus Western equine encephalitis