I figure this app deserves a wider audience.
OTR (Off-The-Record) is a popular protocol for end-to-end encryption, and has been implemented in a number of apps: Signal, WhatsApp, Facebook Messenger, and Google Allo all use OTR with the Axolotl Rachet algorithm.
However, OMEMO offers some improvements over OTR. It enables easy, multi-device, multi-party, offline-capable, forward-secure chat encryption over XMPP.
Using the OMEMO protocol would be interesting enough by itself, but Conversations' additional innovation is that it avoids using the Google Cloud Messaging service without significantly impacting battery life.
The default server is free to use for six months, afterwhich you need a subscription. Or you can simply host your own XMPP server.