Bandaids are what girls with tiny breasts do when they don't want to put on a bra, or if they're wearing something that their bra (or nipples) would show through on. There are some dresses and shirts I do this with: the cut of the back or shoulders is just awkward enough that I can't wear any bra I own without showing. And it's all well and good to be able to say 'well, it's not like I need the support' - until it gets a bit chilly and you get the most awkward goose pimples ever.
And, for yet more information, only marginally related:
Beyond bandaids, some women bind their breasts down with bandages or special devices, especially when cosplaying male characters. There's basically three levels of chest where cosplaying men is concerned:
Small enough to get away with no bra or a sports bra and still look totally flat
Medium enough that people will forgive you the sports bra, or you'll look totally flat relatively painlessly with chest binding
Large enough that nothing will make your chestmonster invisible. You might as well give up now and cosplay a large-titted anime girl. Chest binding will only cause you physical pain and compress your bust about two inches. Not. Worth it.
...I've been having a lot of conversations with friends about cosplay lately, sorry for all the extra info.