I'm in the middle of coding a 'remember me'-equipped login form, and so far the tutorials I've read (partly to make sure I'm doing it right) all say to store the encrypted password in a cookie along with the username. Then, each time PHP checks if the current user is not logged in, check their cookies and look for those values. If the username matches the password, you're in.
To me, this is a gaping security hole. If somebody were to hack the database or somehow get access to the encrypted passwords, they wouldn't even need to crack them. Just set your own cookies and go. Am I correct, or just being paranoid?
My login system uses sessions to keep track of the current user id, and a 1/0 for a quick logged in/logged out check. The user can't edit sessions AFAIK, so this is secure (if it's not, please let me know). I was thinking of just storing the session ID in a cookie, to later resume it, but that's also not secure.
I care a lot about the security of my users, how can I properly protect their information while still maintaining a functioning website?