In addition to showing you which terms are trending on Twitter at the moment (more interesting and relevant than just watching the public stream go by), Sideline lets you create searches that get their own tabs in the interface.
Unlike Tweetdeck, though, which also lets you create searches, multiple Sideline searches can be grouped into bigger buckets, which show up as tabs. You can create a group of searches for all Twitter mentions of your company's various products in one tab, and, for the sake of argument, your competitors' products or issues in another.
Searches can be advanced or simple, with advanced queries almost (but not quite) getting Boolean options, as well as rough sentiment filtering.
A general-purpose Twitter client this isn't. You can't use it to follow the people in your Twitter network, and you can't post to Twitter from it. But it's a handy little tool, and a pretty sweet demo of Yahoo's UI Library. The code is open source. There's more about developing the app on the Yahoo User Interface Blog.