Whether you realize it or not, it's likely that you're constantly using Web apps as you surf the Web. Sites such as Facebook are meant to be left open, and it makes sense to separate them from more traditional pages. Magic Box (free) offers one way to do so, as a standalone browser which can open up any of 15 Web apps (including Facebook, Youtube, Twitter, Gmail, Hulu, and LinkedIn) in different tabs. However, the lack of features makes it less useful than a simple bookmark folder in a more full-featured browser.
Magic Box's browser is just a lightly modified version of Internet Explorer (as is Xtravo Explorer, also from Jawoco), but it's one with absolutely no UI besides the tab interface. The goal may be simplicity, but the program is crippled without a URL bar, bookmarks, and navigation buttons. Without a URL bar, you can't do simple things such as navigating directly to a specific Twitter user's page.
There's also no customizability. The "Home Box" page with links is static, so Web apps can't be added or removed. You can't even add your own bookmarks. In general, Magic Box is so bare that it's more frustrating than useful. If you really like the look of Magic Box, then give it a try. Otherwise, just use a separate window of your favorite browser instead.