Alternatively, one could make it opt-out rather than opt-in. Slashdot does this for your session - you can mark a session as being at a "public terminal", ensuring that you're logged out when your browser session ends.
My problem with the "remember me" checkbox is that I don't want the site to remember my login credentials until after I know that my login attempt was successful. If I mistyped my email address or password (the latter being both easier to mistype and harder (impossible) to verify), I don't want the site to remember that information.<p>Fortunately, my browser usually asks me whether it should remember the login information after the page is loaded.