ChatSecure is a free and open source messaging app that features OTR encryption over XMPP. You can connect to your existing accounts on Facebook or Google, create new accounts on public XMPP servers (including via Tor), or even connect to your own server for extra security.
Unlike other apps that keep you stuck in their walled garden, ChatSecure is fully interoperable with other clients that support OTR and XMPP, such as Adium, Jitsi, and more.
ChatSecure only uses well-known open source cryptographic libraries to keep your conversations private. Other apps may make claims about "military grade" security but, without publicly auditable source code and verifiable end-to-end encryption, you cannot be truly safe.