UPDATED: As far as I know everyone on Twitter can now download an archive of all their twitter activity, there are a few neat things you can do with the data once you’ve got it. For instance, you could upload it all to your website (or your Google Drive) make it public and searchable as I have done http://tweets.sciencebase.com
So, here’s all my tweets dating back to when I first signed up in June 2007 and available for your delectation. A mere 32,000 tweets at the time of writing. By using using the unconverted root file “index.html” from your archive and the attendant CSS files etc you effectively get a browsable web site of your Twitter archive.
Currently, I am hosting my twitter archive on my website rather than Google Drive, I am sure there’s a way to use the drive or perhaps DropBox to periodically download my archive and automatically sync the CSV file from it to my server, but for now I’ll do that manually.