What happens when I use a public computer to check email, and accidentally check "remember me" then log in. Now, using your method, how do I ever clear my login on that computer? Do you then need to have a "don't remember me" checkbox or link?
I think the accepted behavior (at least this is what I have seen on every site that does it) is to perform an automatic login as long as you haven't logged out. Only when you log out does it revert back to force login.
Like I said before, if I have to click a login button every time even if my login details have been rememberd, it doesn't provide much convenience to me because most browsers can remember the passwords as well so what's the point?
As far as implementing it, just execute your regular login procedure automatically if you detect the presence of all the user's login info in the cookie.