Dolphin/xscope, other browsers just use browser menu quit/exit option. The browser app may appear in the currently running apps list after you close it but that's just because android hasn't bothered to clear it yet. It isn't using CPU so it isn't really using battery power and you should ignore it. It would take more CPU and battery power to task kill it. The same goes for any other app. If it has a quit function, use it. Otherwise, you can just move on to something else and Android takes care of it. The exception is poorly designed apps that crash or just won't quit. Don't use these apps. Ironically, an automatic task killer is just this type of app. It runs on startup, runs continuously, and has no quit button.
As for the stock browser, go to menu, view the list of open windows and click the X next to each when you're done...if you're concerned that you're on a page that may automatically reload and use resources. This is a good habit, more or less.
Using a task killer that you run manually makes sense as long as it kills itself when done. But for me, I stay away from poorly designed apps, use quit/exit buttons when available, and I don't use any task killers. On the rare times that I do want to kill something, I just go to phone settings and examine/kill it the built-in way.
I believe that this is the most efficient way to operate android--the way it was designed to run.
