Don't ever do that. Throwing around passwords in the open.
Safest method:
Store the username in a database, in the same row a randomly generated salt value, in the same row a hash checksum of the password including the salt. Use another table for sessions that references the table with user credentials. You can insert in the sessions table when the user logs in a date you want the session to expire (eg. after 15 days). Store the session id in a cookie.
Next time the user logs in, you get the password, add to it the salt for the user, geterate the hash, compare it to the one you have. If they match open a session by inserting a row in the sessions table and sending the session id in a cookie. You can check if the user has logged in and which user it is by this cookie.
Edit:
This method is the most popular in use on most sites. It hits a good balance between being secure and practical.
You don't simply use an autoincrement value for the session id. You make it by using some complicated checksum which is hard to repeat. For example concatenate username, timestamp, salt, another random salt, and make an md5 or sha checksum out of it.
In order to implement a feature that involves user credentials in a website/service there most be some exchange of data related to the credentials between the client and the server. This exposes the data to man in the middle attacs etc. Additionally cookies are stored in the users harddrive. No method can be 100% safe.
If you want additional security you can make your site go over https. This will prevent people from stealing cookies and passwords using man in the middle attacks.
Note:
Involving IP addresses in the mix is not a really good idea. Most often multiple clients will come from the same IP address over NATs etc.