A recently popular new startup that is making waves, namely Secret.ly was quite soon hacked after it was first released, giving the attacker access to the identity of the poster, effectively defeating the purpose of the secrecy. So they said "We take security seriously" and threw a public challenge to the hackers around the world... Or so it seems becase there are no real incentives besides curiosity and pride and maybe some swag from secretly.
On the other hand, the not so known messaging app created by the brothers Nikolay and Pavel Durov. While the latter is well known being the founder of the most popular russian social networking site VK.com, his brother Nikolay is less know and he was the one to device the new communication and open source protocol MTProto for the Telegram. Telegram is non profit, partially open source (the Protocol and API code is open so every one who is skeptical can make sure that it is truly secure) and is absolutely free. It is available for Android and iOS. And if all the above doesn't blow you away yet, there's more. To make sure their implementation is secure, they are running a crypto challenge and the winner will get $200,000 in Bitcoin currency. Now that's serious.