After months of promises, Twitter has finally unveiled a tool to enable users to export all of their tweets if they choose to. The tool is not available to all and, knowing Twitter, it's going to be a slow roll-out.
Only some users are seeing the option, but Twitter is technically keeping its promise of having it ready by the end of the year.
Users that have it enabled will see the "Your Twitter archive" option at the bottom of their settings page on the site. They can request their archive and have it sent to their email address when it's ready.
The archive contains all the tweets you've ever written in a bunch of files and folders. You can view them in any browser by opening the index.html file in the archive.
The option should become available to more and more users, though it remains to be seen whether everyone will see it by the end of the year.