Some program always asks for my login password. I do not know what causes this. How can I stop it?
I presume that you must have turned on the "Auto-login" option on, when you turn it on, to unlock the login-key-ring (the place where your passwords are stored for chrome and other applications), you need to enter the password that you have setup for your account. I always get prompted with this when I am trying to open Chrome for the first time after booting up Ubuntu-Gnome. It asked me to set up the password for this key ring but I believe that it won't ask for Ubuntu Unity and it's the default password that you used to log-in in to your account.
I wouldn't recommend disabling this feature because it will unlock your key-ring without the password. However, here is how to turn it off.