There are many tools and applications to work with Twitter, but right now, I use Twitterfox as my primary tool to interact with my Twitter account. I also have some applications installed like Seesmic desktop, DestroyTwitter, and TweetDeck. But, when I start working with my browsers, I rarely open other Twitter desktop client(s).
Seesmic introduced its web-based Twitter client. If you’re using the desktop version, it’s very similar. The web-based version recreates the desktop application. I tried it, and it looks good. The main reason using Twitterfox is because it offers simplicity with very basic features (updates, checking replies/mentioned, and direct message).
So far, my favorite feature of Seeismic (web-based version) is the Gmail-like style. Simple. And, it’s auto-updated, too.

Of course, if you have wide-screen monitor, you can switch to multi-column interface.