On my HTC MyTouch 4G (Android 2.3.4), twice now the diagnosis for odd failures was to take the battery out, wait a minute, and replace it. (The first failure was loss of network; the second was web sites only partially working, e.g. I could read SE sites but not log in.) Both times popping the battery fixed it, and my provider told me I should do this every couple months as "preventative maintenance". This violates my mental model. So, clearly, either my mental model is wrong or HTC and the folks at T-Mobile are having fun with me. I'm going to start by assuming it's the former.
I power the phone down at least once a week. I think of this as being like rebooting a laptop computer; when it's powered down I don't expect the battery to be retaining any state. But if that's true, why does performance degrade over time? What is my phone doing with its battery during these times? Does periodically powering down do anything useful, like kill long-running processes?
I tried Google and reviwed the "battery" questions here before asking.