I feel very comfortable recommending TextSecure. TextSecure might be the only secure messaging app I feel that way about.
For whatever it's worth: I have no commercial relationship with the TextSecure team, have never worked with them, have never been paid to audit their code, and am only faintly acquainted with Moxie (I've talked to him in person to know that he's extremely pleasant and surprisingly soft spoken, but not more than that).
Trevor Perrin, who worked with the TextSecure project to help design their cryptography, is someone I know a little bit better; it would be safe to say that Trevor Perrin is the only reason I know anything about cryptography, and, given a few bar napkins, I can outline a pretty convincing story that he is the root of basically every TLS vulnerability discovered after Marsh Ray found the resumption bug.
TextSecure is a great project, and if anyone was debating between it and some other cryptographic messaging application, I hope I've made that decision a little easier.