Don't get me wrong, I love being automatically logging in, but what's the point of logging out unless you log out everywhere?
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- Any Stack Exchange user can ask a question
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First thing that comes to mind for me is session fixation.
I think it's currently a fairly serious problem. If I'm logged into any of the SE sites, I get auto-logged into any other one I visit. If I forget to log out of each of them, I'm stuck.
It currently means I can't access SE on a public or shared computer without clearing EVERYTHING. It's a pain.