Tomasz has an amazing extension here. Twitter integration is available for other CMS's, like WordPress and Drupal, but Tomasz's extension goes much further.
After an article post, this extension retrieves the URL for the Joomla! article, converts the URL to a TinyURL interactively, behind the scenes, using curl, and sends the article title *and* the TinyURL to Twitter.
With it, you can help drive Twitter traffic back to your site. It's the modern day equivalent of a ping and it's a good example of how to take advantage of the power of a social network to generate more interest.
I very much recommend this extension. It is well developed and extremely functional.
Good job!