It may be worth pointing out that Opera pushes widgets, small Web pages that float separately and don't look like a browser. While producing a widget doesn't rearrange the browser's behavior itself, it does create a stripped-down page focused on a single purpose.
Step 4 to a better Web browser: Customize content to suit your needs
The information that appears in the browser window is also fair game. In fact, many of today's plug-ins reach right into the DOM tree to modify data so that it's easier to read or interact with. ImTranslator is a popular way for Firefox and IE users to pipe content from Web pages into Google's translation engine. I've always liked Bubble Translate, an extension for Chrome that is relatively unobtrusive and handy, especially for those who need occassional help translating a word or two.
Although it hasn't been updated recently, Poker Eval for Firefox provides a good example of how plug-ins can reach into Web content and provide useful information based on what it finds there -- in this case, the mathematical odds of winning the hand you've been dealt in an online poker room. Another, WikiLook, will pop up a small window with the Wikipedia entry for a selected word.
There are a number of different variations on this idea. CronZilla, for example, loads a particular URL at set times.
For those of us who wither at the thought of clicking on another window to find out whether anyone has sent us email, extension developers offer GMail Checker, which posts the number of unread Gmail messages in your inbox in the toolbar of Chrome. If that's not enough, there's GMail Checker Plus for those who need more email features packed into their browsing experience.