When keeping pets in an aquatic or semi-aquatic environment utilizing a pump for water movement, it is important to cycle the tank prior to adding treasured pets. This helps establish the biological filtration which will help maintain good water quality in your tank. This is usually done for a week prior to the intended stocking date for the tank. The tank is properly filled with aged water, everything is checked to make sure it works, and then some hardy, inexpensive, 'disposable' fish are added.
The hardy fish are fed a normal diet and contribute their wastes to the tank, which break down and feed the newly developing colonies of beneficial bacteria which they brought with them. Any live plants placed into the tank also have a chance to acclimate, and assist in introducing fauna to the tank.
Beneficial bacteria colonies are extremely important to aquatic tanks. They are the primary form of filtration, regardless of what kind of filter you have. Every single surface in your tank hosts invisible colonies of bacteria munching through the nitrogen and other wastes your fish produce. Without this bacteria, an ammonia spike or other such imbalance will kill all the fish.
Of course, you're stuck with the 'disposable' fish, if cycling doesn't kill them (and it shouldn't kill danios, which are extremely hardy and some of the most popular for cycling tanks). Luckily, danios are rather attractive fish that do well in communal situations. I've successfully cycled tanks by adding live plants and aquatic snails, remembering to feed the snails a bit of fish food. It takes a little longer, but live plants in a tank also means that you have another thing taking nitrogen and other elements out of the water column. That's a good thing. Of course, you're stuck with snails after that, but I like snails. They keep my glass clean. If you don't like snails, several fish eat them with relish, including clown loaches and oscars. Actually, oscars also eat fish, but I don't really recommend it. Eating live fish can give oscars parasites.
If you are establishing a vivarium with a moving water supply and live plants, it's still a good idea to cycle the water for a week prior to adding livestock. Humid vivaria are often for amphibians, and they absorb water through their skins. Cycling permits the tank to stabilize and settle before you add tender animals. Again, bacterial colonies will form on the gravel, etc, and the live plants will facilitate the aging process. Add a single aquatic snail for the nitrogen, and you will have a solitary glass cleaner as well. 1 snail = no snail babies!
I know I've sung the praises of live plants this whole writeup, so I'll enter one caveat. Live plants can actually slow down the cycling of a tank because they consume the same things as the bacteria. In fact, some people have heavily planted tanks that cannot handle a sudden large increase in fish load because the bacterial colonies are small due to the large number of plants. Nonetheless, I find adding a few sprigs of anacharis to be beneficial to the tank and the poor 'disposable' fish or snails. The lesson to learn is not to use fewer plants or resort to plastic or silk plants, but rather to introduce fish to the tank more slowly. Always add fish to a tank gradually, and take care not to exceed the capacity of the tank.
Note: In talking to riverrun, I've realized that this writeup is glaringly fresh-water biased. However, cycling is necessary for marine tanks as well. The principles are the same, just the particulars differ.