For aquarists, two factors are important when discussing water - clarity and quality. A glimpse of some of the habitats that fishes call home in this country will reveal that clarity isn't always important and many freshwater species have adaptations that enable them to navigate and communicate in poor visibility.
For many people, terms such as 'gin clear' are used to describe clarity, but this phrase hints at the fact that many crystal-clear liquids can be quite toxic to aquatic life. It's important to remember that clear water isn't always safe for livestock and that because they can't leave the tank themselves, existing fish will often survive in conditions that can harm new additions that are unaccustomed to them.
A visual check will establish the clarity of your water and very experienced fishkeepers can often tell when their pets start showing signs of stress. For most people, however, testing the water parameters is the best way to determine the health of your aquarium. The age of your setup will determine what you should look for - as a general rule, toxins like ammonia and nitrite are a problem for new tanks or those with filter problems, whereas nitrate and phosphate issues are more common in mature systems with mature filtration. For marine enthusiasts there are more parameters to keep an eye on, such as magnesium and alkalinity which are crucial for the health of corals. A discus keeper will want to monitor carbonate hardness or TDS and generally, successful keepers don't like to guess about their conditions too much.
Probably the most important group of people who should be testing their aquarium water regularly are parents, as testing the water before leaving the house means that promises can be made about buying new fish while avoiding coming back empty-handed...
Finally, the biggest argument for water testing is the welfare one. If you can save your pets from premature death, disease or stress then surely you should? Why make the same mistake that everyone else does when a simple test can tell you everything you need to know to give your fish a long and happy life? Given that they never need walking or grooming, won't leave fur on your clothes or chew your favourite shoes, it seems a very modest request on behalf of any pet.