Gwibber is a native desktop Twitter client for Ubuntu. It will post updates to and receive updates from Twitter as well as a host of other services like Flickr, Facebook, Digg, can update your Pidgin status and pull in any other RSS or Atom feed you like.
It will sit in your notification area waiting until you get some messages which it will display as pop-ups in the corner of your screen, and won’t steal focus whilst it does so (take that, twitterfox!).
It is unobtrusive, attractive and easy to use. Theme templates are just HTML and CSS. I recommend giving it a go.
In Jaunty Jackalope it is in the Universe repositories (so sudo apt-get install gwibber will work) but for everyone else you can either follow the instructions on this page (which means you will get future updates) or go direct to the Gwibber PPA page, expand the section with your distro listed and grab the .deb file.