Does politeness mean always acknowledging the greeting?

Do you always reply if someone pm’s you out of the blue? If a friend calls or texts or IM’s, do you always respond? Or do you feel like you should respond, even if you don’t respond?

There was a time when girls in some social groups were taught by their mothers to always accept an invitation to dance. You didn’t want to make the boy feel bad.

It seems to me that a sense of obligation to reply may be present, but I don’t know that. So, do you feel you should reply? Do you reply? If you only reply sometimes, then what is your rule for deciding when to reply and when not to?