Hey Born,
If you close or X out your browser it should retain the cookie in your browser. That means you'll be automatically logged in the next time you visit unless you clear your cookies between visits.
Now, if you're on a public computer (one that multiple people use), you may wish to logout before you leave so no one else accidentally gets into your account. Many banks and financial websites recommend you log out to completely close out the session. That's never bad advice.