It depends on the environment you are in and the image you wish to display.
If I am grunging around the house, I don't mind my bra straps showing. Only my wife will see them, or maybe the UPS guy or a neighbour come to borrow a tool. I am much more self-conscious about my hair than I am about my bra straps.
When out in public, I don't like them to show. If they do because my top slipped or something, no big deal, but I prefer not to display them.
And if I am at a dressy occasion, which is the only time I would wear a dress, I absolutely would not want them to show at all. Basically, when it comes to fashion, I channel my mother: she would have been horrified if her bra straps showed. I avoid spaghetti straps on tops or dresses anyway in order to minimize my broad shoulders, but if I did wear a dress with thin straps, I would consider a strapless bra. I almost have enough to hold one up now!