I'm not (yet) a big Twitter.
The Twitter web interface is pretty simple to say the least. To use it, you have to keep hitting Refresh on your browser. Before you flame me, wait a second.
There are plenty of capable desktop and mobile applications that are much more capable clients than Twitter.com itself. I find that kinda odd but ...
Anyway, as you probably have figured out, I'm a big "cloud" proponent, e.g. Bloglines and Gmail.
While personalizing Gmail, I came across TwitterGadget. The Gmail gadget required 3rd party cookies be enabled which I didn't want to do so I kept looking.
What I found was that TwitterGadget's web interface is good alternative to a fat client for Twitter. That link is at the VERY bottom of the TwitterGadget home page.