That depends on the app. I know a few apps will exit and close down completely. My banking app does that. The Opera browsers have an Exit button that you can configure to be available. However, it doesn't close down all of tabs. I don't use it much anymore, so I have not looked into if it can close down all tabs.
If you want a quick way of switching between certain apps. I think the home screen config is the only way to do it. That will work if you mostly use the same apps all the time. The task manager does list all open apps, but I believe they are ordered by most recently used. The most recently used apps will be at the bottom of the list (on ICS and JB), so you can switch between them more easily. If you have an app you opened, but haven't used in a while (compared to other apps), that app will move up the list.