What diseases do opossums carry?

It depends on whether the creature in question is a true possum, or an opossum, which is quite different.

True possums are native to Australia (and introduced to New Zealand), and they are entirely unrelated to opossums, except that both creatures are marsupials. The only disease a person or a pet is likely to get if bitten by a possum is tetanus from an untreated wound. Possums can also transmit ticks and fleas to household pets. There are no incidences of the rabies virus in either Australia or New Zealand. However, New Zealand possums are subject to a form of bovine tuberculosis which has so far been shown to be transmissible between cattle, possums and ferrets. This form of TB has not been found in Australian possums.

In North America, however, it is a different situation. The body temperature of an opossum is generally too low to harbour the virus: it is possible, although highly unlikely, for an opossum to carry the rabies virus. However, there is at least one documented case of a rabid opossum biting a child, so it can be presumed that in very unusual situations, opossums might carry rabies.