Is aquarium water testing really necessary? In a word - yes! What should be tested, and how often, is not as short an answer. In a newly set up aquarium, water testing is critical to avoid fish loss as ammonia and nitrites rapidly rise. In an established tank, water testing is important to ensure the continued health of your fish.
Test kits should be considered part of the operating expense associated with keeping an aquarium. If you cannot afford test kits, or feel uncomfortable testing water yourself, check with your fish shop to see what they charge for doing water tests. Some offer one free test each month, or will quote you a flat fee for monthly testing. Compare their charges against the actual cost of test kits.
Which aquarium water test kits should you get? In my experience, I've found the following most valuable to fish keepers; ammonia, pH, nitrite, and nitrate. Hardness levels are useful to establish what your levels are, but don't warrant purchasing an entire kit for (unless you have special needs such as a planted tank). Phosphates are worth testing for if you have algae problems. All testing should be recorded in a log or journal so you have a record of what is happening over time.
Testing for ammonia is a must. Ammonia will be elevated during the start-up cycle in a new tank. However, ammonia can also be elevated in mature tanks if the water is not changed regularly, filters are not kept clean, if the tank is overstocked, or if medication is used that disrupts the biological cycle.
In an established tank, an ammonia test should be performed and recorded in a log once a month. Anytime you have sick fish, or a fish death, you should immediately test for ammonia. Any detectable amount of ammonia should be addressed swiftly, as it is extremely toxic to fish.
Aside from new tank syndrome, I've found that pH is the most frequent cause of fish stress, which can ultimately lead to fish loss. Unfortunately, it is usually the most overlooked parameter. Fish cannot tolerate sudden changes in pH. Even a change of 0.2 can result in stress or death if it occurs suddenly.
Know the pH of your fish shop's water, as well as your own, so you can be acclimate new fish properly. Keep in mind that if you use tap water, it has dissolved gasses as a result of being under pressure. Let the tap water sit overnight before testing the pH.
pH can, and will, change with time. Fish and plant waste, water evaporation, topping off water, and water hardness will all contribute to changes in the pH. As a rule of thumb, pH in an established tank should be tested once a month, and any time there is a fish death or illness.
Another factor of pH is the buffering capability of your water. If your water pH changes suddenly, or drifts regularly over time, you should check the KH (Carbonate Hardness) of the water. Consult your local fish shop for KH testing, and for buffering compounds to stabilize the pH level.
During the startup of a new tank, nitrite levels will soar and can stress or kill fish. However, even after an aquarium is initially "cycled", it is not unusual to go through mini-cycles from time to time. For that reason, include nitrite testing as part of your monthly testing routine. Any elevation of nitrite levels is a red flag that indicates a problem brewing in the tank. If a fish is ill, or dies, it's wise to test for nitrite to ensure it is not contributing to the problem. The only way to reduce elevated nitrite levels quickly is via water changes.
Although nitrates are not as toxic as ammonia or nitrites, they must be monitored to avoid stressing the fish. Nitrates can also be a source of algae problems. Nitrates will rise over time and can only be eliminated via water changes. Monthly tests are important - particularly when breeding fish, as young fish are more sensitive to nitrates than adult fish. Test monthly and keep levels low to ensure a healthy tank.
Whenever anyone complains that they cannot win the battle against algae, phosphates immediately come to mind. Phosphate serve as a nutrient for algae, and elevated levels will certainly add to your algae woes.
Although it's rarely discussed, a leading cause of increased phosphates is dry fish food - particularly overfeeding with lower quality foods that are high in phosphates. If you have algae overgrowth, test for phosphates. There are filtering materials available that remove phosphates.