ANDY'S ANSWER: My grandmother used to say, "The way to test if a girl needs to wear a bra or not is to stick a pencil lengthwise under her breast. If the pencil stays, she needs a bra, if the pencil drops she doesn't".
There are different reasons for wanting or not wanting to wear a bra. The most important reason I'm guessing would be for comfort. A bra supports the breasts so they don't move around as much when you are walking or running. Some girls find that a bra protects their nipples from rubbing on their shirts. The sports bra is the most practical kind of bra for support comfort.
Another reason to wear a bra might be for modesty, although camisole or tanktop would serve the same purpose.
Bras have also become part of fashion, aimed at enhancing the look and size of breasts. Bras with underwires and padding to push up breasts are designed to make them look larger and to give a girl cleavage. Young girls often want to wear a bra even when they don't really need it because it makes them feel more grown up.
Although most women choose to wear bras, it's really not necessary if you decide not to. Some people think that by wearing a bra prevents breasts from sagging in later life, but there is no evidence to support this theory. In fact, even if you have a very large bust, you may find it more comfortable to wear a tanktop with a stretchy built in bra as an undergarment rather than a formal bra for those pieces of clothing that need something underneath.