Thing Labs' new browser-based Twitter client allows you to use multiple accounts, monitor searches, share photos, save drafts, interact with Facebook and edit trending topics. It's in public beta, but you can try Brizzly at http://brizzly.com!
This was my default Twitter client of choice before #newtwitter. I love the friendly looking site and expanded media. I also love being able to reply in-line to tweets and mute individuals. Now that the company is acquired by AOL and Twitter is working on their official client, I don't use Brizzly as much any more.
I tend to use Brizzly when the Twitter website is giving me some issues. I like that you can see pictures, videos, and long URLs right in your stream. Also, the mute and draft functions are awesome. A semi-annoying thing is how it pulls up the last several DMs you've gotten and they blink until you attend to them.