As promised by Twitter CEO Dick Costello, Twitter is now letting you download a collection of every tweet you've ever tweeted, beyond the mere 3,200 tweet limit imposed by the Twitter API. If the option is available to you, it can be found under settings. Once you request your archive, all you have to do is wait, and Twitter will send you an email when it's ready.
When delivered, the archive is presented as a zipped HTML file which displays the tweets in a calender-like format, a better deal than a straight-up list of text. So get ready to dive into your own personal Twitter past. Or don't. There could be some embarassing stuff back there.
Check your settings page and scroll down to see whether an "Archive" section exists yet. If it does, you can request a download of your entire Twitter history, from your first tweet on.
Hat tip: BadBlue Tech News.