The odd tech out here seems to be SMS. It's instant and most of the time you'd want messages to be discarded for privacy. But what if you want to save messages? I've been known to type messages into LJ. Someone on the train right now is handwriting SMS messages into a notebook.
Phone manufacturers need to provide a way to save messages to a computer. (Not sure how many already offer this.) And phone companies could offer a service to save messages on a server for a period of time. This carries an increased privacy risk, so it should be an option. But the reality is that messages are no doubt already saved for a period for law enforcement reasons.