Update: 21 November 2016 – I now recommend Riot as the best encrypted messenger, as it has similar security to Signal and it is decentralized, making users independent from any particular provider.
Update November 4, 2015: The app is now called “Signal” on both Android and iOS.
The Intercept: You Should Really Consider Installing Signal, an Encrypted Messaging App for iPhone (or its compatible Android equivalents TextSecure and RedPhone):
The new version, Signal 2.0, folds in support for encrypted text messages using a protocol called TextSecure, meaning users can communicate using voice and text while remaining confident nothing can be intercepted in transit over the internet.
That may not sound like a particularly big deal, given that other encrypted communication apps are available for iOS, but Signal 2.0 offers something tremendously useful: peace of mind.
Unlike other text messaging products, Signal’s code is open source, meaning it can be inspected by experts, and the app also supports forward secrecy, so if an attacker steals your encryption key, they cannot go back and decrypt messages they may have collected in the past.