Telegram is a texting app whose "secret chats" supposedly run on public key encryption or at least Diffie-Hellmann key exchange to use encryption. Other than that, I don't really know about something similar that has actually taken off.
The problem with encryption is that your ordinary person still doesn't consider themselves affected by the massive number of parties who might want their data, whether they are governments, corporations or independent individuals. They think having an honest, law-abiding lifestyle is a total safeguard from mass surveillance. I'm just a 9-to-5 office worker, why should I be affected? This is why your ordinary layman is not concerned about crypto. Admittedly, however, the NSA mass surveillance scandal, and its secondary exposure of other mass surveillance programs like Google or Facebook's, have resulted in laypeople taking privacy and security much more seriously. For example, when Facebook purchased WhatsApp, there was a mass migration of people from WhatsApp to Telegram.
There is, however, a second problem associated with crypto: people view it as hard, arcane and highly academic stuff, like rocket science or quantum mechanics. Just look at how wrong can Hollywood get crypto. Therefore, people just don't use it. Even with tools that simplify using cryptosystems as much as TrueCrypt, GPA and Enigmail on computers, or APG on smartphones, people still think crypto is hard to use by an end user and therefore they don't use it. It really doesn't help that the user himself must take measures to make sure crypto will actually work. When people share passwords as a ritual of love and write them on a Post-it on the monitor, you have large numbers of people who might as well be sending absolutely everything in plaintext.