Signal
Signal is the iOS app made by the Open Whisper Systems project. Like TextSecure, it provides complete security to protect users from any external snooping. It now supports sending and receiving messages from TextSecure, which runs on Android. The app uses the same encryption technology as its Android counterpart.
Telegram (secret chats)
Telegram is a messaging app available on iOS, Android, and Windows Phone. It was created by two brothers who helped launch the huge Russian social network VK (formerly VKontakte) in 2012. It offers two different types of chat options: normal chat — which has chats stored in the app’s cloud, and “secret chat” — which uses end-to-end encryption. While the normal chat does not follow the most scrupulous securing processes, if a users sends only secret chats, that person ought to have their security bases covered.
Silent Text
Silent Text is the secure messaging app from Silent Circle, one of the better-known companies building secure communication programs. Most famously, the company built the supposedly ultra-secure BlackPhone, which purports to be an NSA-snooping proof mobile device. Silent Text is said to be completely secure, using the best encryption practices available. But it does require a monthly subscription, which starts at $9.99.
Gliph
Gliph is another messaging app purported to be completely secure. Its spin differs from most other apps, however, in that it also facilitates Bitcoin payments. The app allows users to anonymously send amounts of the digital currency to other Gliph users. It also has special message features including the ability to set a message expiration time as well as schedule messages.
Crypto Cat
Crypto Cat is an encrypted message-sending app that has been known for being very easy to use. It, like all other acceptable secure message apps, employs end-to-end encryption. It creates private and secure chat rooms for people to access and hold non-surveilled conversations. So a user creates a chat with a unique name and only users who know that chatroom's name can drop in. They make their own one-off screen name for the chat session, so CryptoCat can be used for anonymity. It’s available to use on both iOS and desktop.
Bleep
Bleep is an app made by the people behind BitTorrent, and it's not finished but is available for public testing ("alpha" in developer lingo) . It differs from other messaging clients in that it sends messages directly from user to user without using an intermediary. This means that no server or company is picking up and potentially collecting metadata about who is using their service. Bleep is still working out some of its problems, but it has early reviews of the app have been positive. Right now it’s only available on desktop or Android, although an iOS version is said to be in the works.