I'm more comfortable without a bra and since I have small breasts I have used that as an excuse to skip it when I can, more at home I admit. There are times in the summer when the temperature is high that I'll go out braless so yes, accidents have happened to me too.
My bikini top has accidentally come off more than once. I had a nip slip while dancing at a friends party, one of my straps was constantly coming down so at some point I left it there and of course the accident happened. I'm not sure how many people saw it since it was crowded and we were dancing. The juciest story I have is while I was waiting in line at the mall to get something to eat/drink, I was braless and a young guy beside me got interested in my side cleavage. When I noticed him, I raised my hand slowly to fix my hair and gave him a good look of what he wanted. About a minute later I did it again!