Apparently realizing that this is starting to become a problem for many users, Facebook has just announced an overhaul of the feature. Most importantly, at least from my perspective, you’ll now be able to filter out updates from Groups and Events into the “Updates” tab (where messages from Fan Pages currently go), which should leave your Inbox itself open to only messages from actual people.
Facebook describes the upcoming changes in a blog post:
“The new Inbox design gives you more control over organizing messages and choosing which messages you receive. You'll notice that there are now filters at the top of your Inbox to help you identify unread messages as well as to report any spam, or unwanted messages, you may receive …
To find specific messages within your Inbox, you can type a keyword or a friend's name in the search box in the upper-left corner of the screen.”
The new feature isn’t live for everyone yet, and might not be for a few weeks. Facebook has provided this preview image for what the updated Inbox will look like: