Working with D7, I want extra statuses for nodes, such as "unpublished," "published," "draft," but also "received," "under review," and "approved." What's the easiest way to accomplish this?
If you want to add additional 'on/off' style switches to an entity or node like Published -> Unpublished and Approve -> Rejected I would recommend looking into the Flag module.
there is also the Workbench module if you need more of an editorial flow with approval processes:
... a customizable editorial workflow that integrates with the access control feature described above or works independently on its own