How to close (shutdown/kill) the Android web browser?

Closing the browser has no benefit. The android subsystem manages the memory on the device really well and will free up memory from background applications if it needs it. As I understand it, it does this by saving the application state in a database on disk. If you run the application again, it can then rebuild its state from the info in the database.

If you want to stop the browser from downloading and you can't see the "Stop" button, press the menu button. This will bring up the address bar allowing you to press the stop button. Although if the address bar has disappeared then chances are your phone is not downloading anything, unless the site you are on has Javascript on it which is causing it to refresh elements regularly. If this is the case you are on your own.

Applications are built to save their state to storage _at_any_time_, and to restore themselves from that state. They are also built to be closed by the OS at any time (e.g. when it needs the room for something else).

AFAICT, all applications share the same screen stack: opening an application's page "over" another one simply adds additional pages to the stack. The Back button just pops the topmost page off. The Home button pops all the pages off the stack.

The applications are still running and, if they are written as directed, will keep their previous state when you explicitly open them again. The difference between an application stored and an application waiting in the background is less than in a desktop OS.

Cheers

The android designs says that when the user 'goes away' from the application the app should keep running for a fast start and for background music playing etc.

This means that what you're asking for is against the nature of android. Applications themself could choose to close themselves after you click 'a close button'. Since applications have to come up with their own solutions you can image that there is no 'one button solution'.

Using a taskkiller is a solution for this problem. A single program in the widget list to kill all unneeded applications for a performance and battery boost is a great help. I'm using Advanced Task Killer set up to keep my most used applications but to close all other rarely used apps.

There might be a browser with a close button but the one I use doesn't have a close button. Then again keeping open the page I last visited is a welcome feature.

You shouldn't want to close applications manually. Just stop loading the current page with the Stop menu item, and use the Home key. This will leave the app running in the background, but without costing power or wasting your download limit.