Epistolaire — Open Source Productivity App

Epistolaire dumps SMSes AND MMSes AND their photos to a JSON file on the phone storage (so you can copy it whatever way you like, rsync, Syncthing, ownCloud - you name it). There's a tool to convert it to pretty HTML pages if you want to without effort. And if you know a little know a tiny bit of development, the JSON format is straightforward to use.