Increased stress reduces a fish's ability to ward off diseases and heal itself (e.g., if its fins get nicked, or parasites get introduced into the tank with newly purchased fish). In addition, stress reduces a fish's ability to breed successfully and shortens its natural life span. A small amount of stress by itself is not usually fatal, but as stress levels increase, a fish's ability to cope with it decreases. Thus, one of the most important goals of a fishkeeper is to remove sources of stress wherever possible.
It should be noted that eliminating stress does not guarantee that your tank will be healthy. But it significantly increases the odds. Many netters boast regularly about how they've kept fish (apparently) ``healthy and happy'' for long periods of time under (apparently) highly stressful conditions. Such aquarists are sitting on a time-bomb; the not uncommon followup story will refer to one fish getting sick, then another, with an end result of multiple fish deaths. Reducing stress simply increases the likelihood that a tank will stay healthy (much the same way as eating right, exercising and getting the proper amount sleep is generally associated with a long healthy life for humans).
Nitrogen compounds (ammonia, nitrite and nitrate) have varying degrees of toxicity and are stressful at all levels. Ammonia is toxic in low concentrations and severely stresses fish under ANY concentration. Consequently, a healthy aquarium must have an adequate biological filter that quickly converts ammonia to nitrite (and nitrate). Although significantly less toxic than ammonia or nitrite, nitrate also stresses fish. Thus, a means of removing excess nitrate (e.g., through regular water changes) helps keep an aquarium healthy.
The water temperature of your tank should match the needs of its inhabitants. Keeping water temperature too cold or too warm for a particular species will stress those fish. For example, goldfish prefer cooler temperatures (under 70F) than most tropical fish (goldfish survive winters in ponds where temperatures approach freezing), guaranteeing that a tank containing both goldfish and tropicals will either be too cold or too warm for some of the inhabitants.
Some fish prefer soft water, others prefer hard water. Keeping a soft-water preferring fish in harder water (and vice versa) is stressful.
Some fish prefer acidic water, some prefer alkaline water, others prefer water with a neutral pH. (Some fish don't care too much.)
Some fish live in brackish water conditions; they will do better in water with a small amount of added salt. Other species are extremely intolerant of salt. Add salt only if all of a tank's inhabitants can tolerate salinity. Mollies, for example are known to like salt, whereas many species of catfish tolerate no salt at all. In general, fish lacking scales (or having small scales) don't tolerate salt well.
The amount of physical space required for a particular fish depends on its species. Some fish do just fine in a 10g tank, others need 100g or more. Keeping a fish in a tank that is too small for it increases the level of stress (on everyone), frequently leading to increased aggression among tank inhabitants. Note also that the amount of space required may change should fish pair off to breed. Cichlids, for example, claim a portion of the tank for themselves when in breeding form, chasing away any fish that encroach on their territory. Thus, the onset of breeding behaviors frequently increases stress levels.
Not all species of fish mix well with others. As an obvious example, most cichlids will eat smaller tank inhabitants (e.g., anything they can fit in their mouths). Even if too big to be eaten, however, peaceful fish will be stressed if kept with aggressive fish that chase them around all day. Moreover, many fish communicate through behavior and body language (i.e., cichlids frequently establish a ``pecking order'' in which one fish is king). Fish of one type of species may not recognize the signals given off by others, guaranteeing continual strife.
Some fish school in nature, spending their entire lives in large groups (rather than individually); they never feel comfortable or ``safe'' when kept by themselves. Cory cats for example, do better in a tank with 6 or more other Corys than they do by themselves. While it may be tempting to buy six different kinds of fish, this may not be ideal for the fish themselves. The opposite can also be true. Some fish are more aggressive towards members of their own species (e.g., mating behaviors), whereas they may not feel threatened by other species and pretty much ignore them.
Fish need oxygen, and some fish are more tolerant of low-oxygen water than others. Water with insufficient oxygen stresses fish. Note that as the water temperature goes up, the amount of dissolved oxygen in water decreases.
Poor nutrition also causes stress. A healthy diet is a varied diet, and one should avoid using old foods in which vitamins and other nutrients have broken down. ``Old food'' includes food that has been stored in hot places, been exposed to air (not sealed), etc.
The ``cure'' of adding medicines to tanks is often worse than the original disease. Medications that kill bacteria, parasites, etc. are usually not too discerning: they may also kill your nitrifying bacteria (now you REALLY have a major problem) or be toxic to the fish themselves. For example, some species of fish do not tolerate certain types of medicines at all. Adding such medications may weaken healthy fish to the point that they become susceptible to the original disease.
Adding untreated water to your tank may introduce chlorine or chloramine, both of which are toxic to fish. Be sure to treat all water prior to adding it to your tank.
Sudden changes in water conditions can be stressful. Within limits, most fish can adjust to sub-optimal water conditions (e.g., wrong temperature, wrong pH). However, fish have difficulty adjusting to a SUDDEN change in water chemistry. Thus suddenly raising (or lowering) the temperature, changing the pH, changing the water hardness, etc. stresses a fish. It is more important to keep the water chemistry stable over the long haul than to keep keep water conditions exactly optimal.
In summary, many factors lead to fish stress. Minimizing and eliminating sources of stress increases the chances of keeping tank inhabitants healthy. The exact amount of stress an individual fish can take depends greatly on what species it is, its age and size, etc. A stressed fish is a weakened fish. Although it may appear healthy to the casual observer, it will be more susceptible to disease, injury, etc. In contrast, healthy (unstressed) fish will be able to ward off disease and infection on their own. Thus, the appearance of disease in a tank is frequently brought on by ``poor water conditions'' that leave fish with weakened immune systems.
Common symptoms of stress include: