If twitter's default archive feature can't satisfy you.... twDocs gives you a flexibility of exporting tweets, favorites, mentions, direct messages and search results.
@joelchaudy Twitter's export doesn't work, or at least I've tried repeatedly over the course of a number of months and never managed to catch it working (including again today).
twDocs uses the Twitter API, which works fine, although it does get limited to your 3200 most recent tweets.
twDocs
twDocs