I don't want to accept a cookie!
A lot of people are paranoid about cookies, and not without reason, but the simple fact is that this is how you create persistence in a stateless protocol. If you don't want to use cookies, you don't have to. You can still post (either anonymously, or by entering your password each time you submit a comment) but you will not be able to use all of the advanced features of the site (i.e. story filtering, customized Slashboxes, user preferences etc.). If your paranoia requires you not to use cookies, this is the sacrifice you'll have to make.
Why do I keep getting randomly logged out?
Make sure that you log in to http://nooface.net, and not http://www.nooface.com. It's annoying, but it makes a difference.