Confide
From Just Solve the File Format Problem
Confide is an app that supposedly offers completely secure and self-destructing messaging, with no way of saving a copy of anything so that the content of messages remains "off the record". Even attempts to take a screenshot are supposedly defeated. (But what about taking a picture of the screen with a different camera or device?)
Messages are end-to-end encrypted, and can be sent to a phone number or e-mail address.