This computer I am on, a free for public use behemoth; has kept me signed in. For instance, this morning when I arrived, (this is at a coffeeshop), I am logged in already.
  "Good morning fisher, you have 13 messages...",etc.  How does that work?

Fisher,

Your login is handled with cookies.  You set how long you want to be logged in for at the bottom of the page next to the login.  The default is 6 hours.  This sets the lifetime of the cookies on that PC.

For your own protection and that of the community, be sure to always log out when you leave a PC that others have access to.  Otherwise anyone could get on that PC and trash the forums logged in as you.

They could cause all kinds of grief if they were so inclined.  Posting spam, or harvesting information from the members profiles are just a couple of the possibilities.

Treat your login like you would for your online banking.

We spend a lot of time here making sure the forums are secure but it is very important to keep your login secure, or none of that matters.

I just changed the default login time to until the browser is closed.