Absolutely not. Your breasts have to be really tiny though, AA Cups. Any larger and over time, if you didn't where a bra for a long time, then your breasts would start to sag. However, if you didn't where a bra, for say a week, it's not going to affect their level. Women with very large breasts have to where a bra, otherwise they get chronic backache.
Actually, it is the bra that gives a big breasted woman back ache. Without it there is no pressure on the shoulders, neck and back. When just hanging they are moving around which can be annoying but it's not harmful. Sag they will anyway due to age.
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