A good general rule of thumb is 'keep your water clean and your filter dirty' and this is really the secret of successful fish keeping. Although good filtration will keep water crystal clear, it is important to remember that although clear, it may be full of the accumulated nitrates, phosphates, pheromones and other byproducts of daily life inside a fish tank. Properly carried out, a water change is always beneficial and if you follow a good regime of regular weekly 25% water changes your pets will prosper. Old water is great for fuelling algae growth and making your tank look tired as well as depressing the immune systems of your fish. Water change rates can be tailored to your stocking levels and feeding rates - messy fish such as large cichlids and goldfish thrive on large frequent changes, whereas Tanganyikan cichlids and reef tanks like smaller changes of around 10% at a time to ensure more stability.
Filters need to be dirty to work properly but there is still some regular maintenance jobs to be done. Biological media such as foams or ceramics need a rinse in water from the aquarium when they start to slow the flow rates appreciably. If you have the option of cleaning 50% of your media at a time, you can make this a more thorough clean but always use aquarium water and never expose mature media to chlorinated tap water. By contrast, chemical media such as carbon or phosphate removing resins become less effective when dirty, as bacteria will literally seal them and prevent them from working. Mechanical filter media such as floss, will work best when kept clean and changed at regular intervals.
Depending on various factors, a monthly rinse of filter media coinciding with that week's water change might be the ideal basis for a regular maintenance regime.