If you're using Internet Explorer, go to Tools > Internet Options > Privacy and set your level to medium. That's where mine is, anyway. You can also click on Sites and specify if you want a particular site to use cookies.
However, have you checked the "Remember Me" box when you've logged in? Your computer is probably accepting cookies. Unless you've told it not to, that's the default. If you don't check the "Remember Me" box you'll have to log back in every time you open a new window or come back to the site. Sometimes I log out and then forget to check that box. It's very annoying. But if you check it, you should stay logged in until you delete your cookies or you log out and forget to check it.