On mobile there are various options. The apps which are likely to be most secure are ones which have end-to-end encryption enabled by default and which can also be onion routed via Orbot. End-to-end encryption secures the content of the message and onion routing obscures the metadata, making it hard for a passive adversary to know who is communicating with who.
This is one of the more sensible comments on here. I personally use Signal for friends/family and matrix (element.io) as an IRC replacement.