Writing for the New York Times, Jenna Wortham suggests that snapchat, an app currently associated with, among other things, teenage sexting may in fact herald a more widely useful feature of messaging, i.e., vanishing after the message is received. See full NY Times article. While this seems radically unique, it is basically what our mental image of impromptu messages should be - quickly delivered and quickly discarded.
Years ago, working with a global IT consulting firm, I discovered that instant messaging (IM), which was relatively new, was very popular with employees in this high-tech firm because they believed that, unlike email, the messages were not recorded on company servers. In reality, most message applications are more like 'email lite,' meaning they are backed up on memory drives and stored for a long time. But the perception of invisibility to others was appealing then, just as it is now with apps like snapchat.
Interestingly, and somewhat uniquely, now-you-see-it, now-you-don't messaging could be considered a hybrid form of connectivity, that is a Type 3 disconnect for the sender (they control the connection) and Type 2 disconnect for the receiver (the connection is controlled by others).