A more current fork of this add-on can be found here: https://github.com/click-rain/EE_Twitter/
TGL Twitter is nearly an identical port of EllisLabs Twitter Timeline plugin, however TGL Twitter has a CP Backend, allowing a user to authenticate with Twitter using oAuth.
The initial reason for building this was because Twitter's Streaming API, which does not require authentication, limits your request by IP Address. On a shared hosting setup, where many sites can be run off of one IP Address, this presents a problem.
The syntax for the modle is nearly identical to that of the Twitter Timeline plugin, so please refer to that for template tag questions.
This functionality of this plugin could easily be expanded to use more of Twitters API methods, I just originally needed it to display tweets.
Please see: http://expressionengine.com/downloads/details/twitter_timeline/
keep in mind that all tags use {exp:tgl_twitter} instead of {exp:twitter_timeline}
Please take note that on some API calls, such as user timeline, if the API does not detect a valid oAuth token it will just default to the unauthenticated API conditions. An example of this is if you install the module, then add in your template tags without authenticating first, data will still be shown. However, this data will be rate limited to 150 and is returned based on unauthenticated API conditions.