OceanLake:
"Don't forget" instead of "Remember"
"Don't touch that" instead of "leave that alon"
Etc.
Why?
As a novelist, an English teacher, and a bit of an everything else (just a bit though), I'd prefer to ask "Why not?"
Psychologically speaking there's the idea that by saying "Don't X" someone is giving a command that's more likely to be remembered than something which sounds more permissive or suggestive like "Remember" or "Leave that alone." Whether or not this is good or bad in the eyes of the viewer is irrelevant unless it's articulated to the person saying "Don't X," and even then it assumes they're in a position and mindset to care about such a thing.
Linguistically speaking there's a whole plethora of reasons why one would use differing phrases to express the same idea. Whether it's for emphasis, or variations, or consistency, or because you believe one way is simply cooler than another way. Colloquialisms, regionalisms, idiomatic expressions, rhetorical nuance, and even dramatic timing are all perfectly valid reasons for using "Don't X" instead of "The opposite of X."
Philosophically speaking it could be that we as a society have been driven to focus on the negative aspects of life, or perhaps we are programmed to do so from birth. Perhaps it must be a conscious effort on the part of the speaker not to use "Don't X" because such a thing comes to use before any other usage, and we must retrain ourselves to think in ways different than those we have grown up with. Or maybe the individual has just been conditioned through their humours to believe not that "Don't X" is negative, but that it has a more positive connotation than other commands because it involves the word "Do" (albeit in conjunction with the word "not").
And, just as a guy speaking, why not?
