Bacterial infections among tropical fish are overwhelmingly not caused by Fish-TB, and in the vast majority of cases the bacteria involved are otherwise harmless species involved in the breakdown of organic matter in the aquarium.
In the case of spiny eels for example, the classic situation is where the spiny eel has been kept in a tank with gravel (as opposed to sand) and the gravel has abraded the skin, wearing away at the mucous and the surface layer of skin cells. As skin cells die, opportunistic bacteria move in to digest them, just as they would digest away at dead skin cells on the substrate or in the filter. Normally the fish's immune system would fend off these bacteria, keeping them away from healthy cells, but if the fish is stressed, because of poor water quality for example, this doesn't happen, and the bacteria start eating healthy cells. As the bacteria multiply they causes blockages in the capillaries, stopping blood getting to nearby cells, killing them, and providing yet more food for the bacteria. Associated symptoms include decay of fin membrane material,
pop-eye, especially bilateral (both eyes) pop-eye, and abdominal
bloating (oedema or dropsy). Once dropsy develops, things are very serious.
This is more-or-less what happens whenever we're dealing with
Finrot or some other opportunistic bacterial infection. If left untreated, the bacteria eventually get into the bloodstream, circulate around the body, and cause a systemic infection of the fish described as blood poisoning, or
septicaemia. Prompt treatment of Finrot will prevent septicaemia, but once established, septicaemia is almost always fatal, though large fish like koi might be treated successfully by a vet.
In short, Finrot and septicaemia are
allowed to happen rather than caught, and both are easily prevented. A balanced diet, good water quality, and avoidance of physical damage (such as scratches and bites) will all prevent Finrot; should Finrot develop anyway, prompt treatment with the right medications should fix mild infections before septicaemia develops.
Mycobacterium infections of tropical fish are very rare. It's impossible for aquarists to distinguish a
Mycobacterium infection from plain Finrot without recourse to a microbiology lab. This cannot be stressed too strongly: any aquarist who tells you they can spot a
Mycobacterium infection from external symptoms alone doesn't know what they're talking about. The symptoms of all bacterial infections are very similar and there's lots of overlap between different diseases. The only real difference from a practical perspective is that
Mycobacterium infections won't respond to Finrot treatments, including antibiotics.
Mycobacterium marinum is very rare indeed, and probably the most well-known disease most aquarists have never seen. So while it is infamous for being among the few fish diseases that can infect humans, it's far less likely to cause problems than something like
Salmonella poisoning.
Salmonella bacteria thrive in the warm, damp parts of aquaria where uneaten food and other organic wastes can develop. Although not a common problem by any means, the frequency with which people get
Salmonella infections from fish and reptile habitats is sufficiently high that it should be taken into account. It's the prime reason why you should wash your hands after doing stuff inside the aquarium. As ever with
Salmonella, the risks are greatest for certain groups of people with weakened immune systems, and if you're concerned, you should ask your doctor for advice.
I happened to edit
an article on bacterial infections of tropical fish for Wet Web Media, and alongside discussing Fish-TB and Mycobacterium infections, gives some practical advice on diagnosing, treating, and avoiding bacterial infections. It's not an easy rear by any means, but it was written by a microbiologist and is based on science rather than hearsay, so I'd strongly recommend you review the piece if you want a thorough understanding of the topic.
Viral infections of fish aren't common at all. Many are species-specific and only attack one species or a few closely-related species. The classic examples of these are
Dwarf Gourami Iridovirus (DGIV) and
Koi Herpes Virus (KHV). In both these cases the virus is highly contagious, and dwarf gouramis for example are fish I would never recommend simply because getting virus-free livestock is becoming increasingly difficult; one report by vets put the infection rate of dwarf gouramis from Singapore at 22%.
The only "common" viral diseases that attack different fish species are
Lymphocystis and
Fish Pox; the former tends to go for "advanced" fish such as cichlids and marine perciforms, while Fish Pox is most commonly seen among carps and their relatives (minnows, goldfish, etc.). Both appear to be triggered by environmental issues, and treatments, such as they are, involve optimising water quality and providing a healthy, balanced diet. The symptoms of both are similar, with Lymphocystis producing textured, off-white to light brown lumps while the lumps that form when Fish-Pox is the cause tend to be more smooth and pale, rather like wax.
In short then, virtually all the bacterial and viral infections your fish are likely to catch are going to develop only if you let them. With the exceptions of DGIV and KHV that plague even the best fishkeepers because they're so contagious, almost all the other diseases of this type are triggered or allowed to develop because the fishkeeper neglects some aspect of fish maintenance. Distinguishing between the various diseases is difficult, and will require help from your vet.
Cheers, Neale