1) The bra can (read: must) reduce the bouncing (yes also flatchested girls' breasts bounce), which helps preventing the breast tissue from damaging.
2) The nipples might not show through their shirt when it's cold or whatever reason there would be causing them to be able to see through the shirt.
3) If you have small breasts a (well-fitting) bra gives a nice shape to your breasts. (And if you wear a push up it can make them look bigger and give you more cleavage).
By the way:
Myth: 'A bra can prevent your breasts from sagging' or 'If you don't wear a bra your breasts will sag'.
This is not true. Actually, a bra should be avoided as much as possible (yes you should wear one when you go outside, but for example when you go to bed you shouldn't wear a heavily padded bra or something), because the bra takes over the function of your pecs, causing them to weaken. Result: your breasts start to sag.
Yeah, due to gravity bigger breasts will (read: have the possibility to) sag more easily, but genetics and the condition of your pecs play a big role as well.