The most privacy-invasive Facebook feature is, unfortunately, one that you can't turn off. But do not fear — there are plenty of work-arounds! We're talking about the "seen by" or "seen at" feature in Facebook messages. Once you've read a message from anyone (friend, foe, or otherwise), they will know that you've seen it, and they will certainly know if you've seen it, then deliberately chosen to ignore it.
But where there is a will, there is a way! These crafty developers created extensions that will prevent the "seen" icon from showing up.
If You Use Chrome
For those of you on Google Chrome's browser, try Facebook Unseen. The extension blocks the URL that sends the "read receipt" to Facebook messages. It essentially marks all of your messages as unread, and you can choose to mark as read when you're ready to reply. The downside? Unless you want that "seen" message to appear, then you'll have an eternal notification for unread messages.
If You Don't Use Chrome
This takes a little bit of tinkering. Install the AdBlock Plus browser extension and then add this url "facebook.com/ajax/mercury/change_read_status.php$xmlhttprequest" to the extension's custom filters.
For even more options, check out this StackExchange thread.