"We really messed this one up. When we launched News Feed and Mini-Feed we were trying to provide you with a stream of information about your social world. Instead, we did a bad job of explaining what the new features were and an even worse job of giving you control of them. I'd like to try to correct those errors now."
The new controls don't allow Facebook users to completely hide their feed from other users, or hide others' feeds. However, what is shown in the Feed can be limited to a bare minimum of items that can hardly be construed as privacy-invasive. This include groups, events, networks, profile removals, status updates, notes, and photos you are tagged in. The Feed obeys the "rules" of profile and limited profile privacy settings, as well, so only people who can see your profile can see items about you on their feed.
It's not perfect, because you can't completely remove the feed. You can, however, remove individual items from your feed. So if you don't make changes too often, and you click the "X" next to them in the feed when you do, you can get pretty close to completly voiding the effects of the Feed.
Good job, Facebook community.