I like Android, but the back button is totally useless to me. It only works in the simplest of cases, namely when opening an app and not navigating beyond that, I know I can press the back button to get to the home screen.
Otherwise, my workflow basically goes: press home button, use the task manager to kill everything, then visit an app and navigate top-down to where I want to go. Rinse and repeat for the next app. Like others have been saying, the back button is inherently either arbitrary or confusing, and I don't know how to fix it.
It should be replaced as a permanent UI feature with a task switcher button. I don't know how a modern operating system can get by without some sort of taskbar equivalent. I need to know what apps are open, and be able to navigate to them and close them as needed. Why has this not been implemented? I'd suggest putting this into the slide down top bar if there weren't full screen apps that totally break this function. Therefore, I suggest replacing the back button with a task switcher. I won't be holding my breath.