It's an excellent question and I'll try and answer this one. It's a subject of great interest and importance to everyone involved in animal care, all pet owners- immunolgy is also a research obsession of mine right now. My older brother is an internal disease specialist in London (that's diagnostic GP to Brits) and my younger brother works for the Ministry of fisheries -UK and Boston based.
I have put this question to both of them and will try to fuse their answers with my own research best I can.
First of all the basic answer for those who don't want to read the whole loonywhack or have little time is that yes there are a very few possibilities of transmission
from humans to fish. But with regular hand washing before and after we are extremely unlikely to do so. Vice versa fish to human is also possible (zoonotic infection is where the fishes disease is transferred to humans). Presently the only 2 disease transmissable from fish to human are both bacterial and are known to us as TB and Vibriosis. Both, are to date treatable.
Next its important to understand the four main threat groups we are dealing with. Each group presents a different potential threat for human>fish transmission reasons which I'll try to explain.
1. PARASITES (dangers for humans to pass to fish)
These have the least threatening transmission possibilities.
Basically this is because parasites need a host (hence the name) and 99% of the time parasites are
host specificmeaning that they are very picky about who they live with! this is a survival instinct because almost always without the appropriate host for their needs (fish slime coat, gills etc) they will die off. Because many parasites are also
organ specific (notice how all the parasites have afavorite resting place internally or externally on the fish) we can be assured that since people have a rather distant, the most distant in fact, body make up/DNA and organ structure from a fish it is unlikely that we can transmit a parasite to our fish that will thrive on the fish.
Howeverit is entirely possible and does happen rather often, that a parasite living on an animal closer in the species chain can attach to a fish and cause damage. Animals including our pet dogs and cats can harbor parsites that are unseen and cause them no damage but can be dangerous to fish. In this case the animal is called a parasite transport host. Avoid having your cat put its paws in the fish water!! Many such transferred parasites may still not have found their perfect host in a fish- and so one of 2 things will happen.
Either, the parsite will quickly die off OR the parasite will attach to the fish (or be freeliving depending on parasite type) and in a desparate survival bid will mutate to try and adapt to the new host. In this case the fish will display very strange symptoms (not found in many reference aids).
2. VIRUSESThese are the smallest germs. Almost all viruses that humans have are not equipped with the same cell structure to infect fish. Viruses are strongly host specific. The cat HIV virus (FIV) is not transmissable to humans for example and so on down the species chain. Very occasionally however viruses will mutate and flip species preference as inSARS and Ebola (I think) and bird flu. Strong immunity is more important to fight viruses than any other germ because there are no cures for viruses. All we hav eare meds to relieve symptoms and alleviate discomfort and we rely totally on the fishes original immune strength (so important to look after).
The only viruses that can cross to fish from humans are the cold/flu viruses that are easily killed by washing hands if you have acold before putting hands in the water. Just to be safe never sneeze in a tank. Chances are the human virus would not affect the fish BUT mutations can happen as explained in 1. and the cold viruses (and the measles virus) are relatively similar in cell structure to the virus that causes lymphosystisis and carp pox in fish.
3.BACTERIAMost bacteria are actually not pathogenic. One of the main probs with bacteria is we kill the good ones with the bad. In doing so antibiotics which cannot differentiate have caused the bad ones to become more virulent. The good bacteria are our immune allies.
Human bacteria are thought not to pose a athreat to fish. (Again washing hands before and after is advised and never swallow tank water.)
4. FUNGIFungi are the plant type germs - mould and yeast are examples. Fungi that affect fish are water dependent. So fungi that affect people will not ususally affect fish. However cotton wool disease bears a very close resemblence to athletes foot so there is still a potential mutation possibility. I don't think we are sticking athlet foot feet in our tanks though and again a simple hand wash is very effective.
I think that covers the basics. I hope it answers some fears. One bonus peice of trivia: if you cannot wash your hands did you know that clapping your hands very loudly for 30 seconds kills most germs?
Here's to safe and healthy tank life