Message Exporter for Android
You can easily set the format type and what to be included in the export. After you are done, you can also share the file, for example, attaching it as an email.
The application currently supports exports of plain text and json files, with more being added soon.
You can also change the contact's and also your own name on the export, numbers to be included, message dates, the message count and also the export span (to/from dates).
The source code is also available on Github: https://github.com/parhampb/MessageExporter