I installed Skype on my wife's phone (HTC Desire), played a bit with it and then exited using the back button as suggested in other question. I can still see her account saying she is logged-in though. How can I exit Skype so that it really stops running?
In the Skype app, press Menu -> Sign out, or use the Sign-out button on the top-right corner of the app's home screen, then confirm.
Try signing out first. And than back button.
Well first off. Theres no true way to stop it. Secondly, The way I do it. I sign out of skype first. Then, i use the manage apps or task manager. Stop the app first. Then, make sure it has been cleared from the cached background processes. A phone restart might be required to start the app again or other apps. I am fine with having to restart my phone. It gives me the chance to control everything I do on it.