How "submitted", "to appear", "accepted" papers are evaluated in a CV?

It's a tiered system:

1. Peer-reviewed published articles. Published means published in any form, so it includes papers in all states published online on the journal's website, including “in print”, “ASAP papers”, “just accepted papers”, etc.

   That's top notch: it demonstrates your ability to perform research, write it up and publish it. Those are key requirements for the job.

   1b. Peer-reviewed accepted papers. All search committees I know will assume good faith, and accepted papers not yet published (thus without proof) are considered as good as published papers. If you want to (and the application format allows for it), you can actually join a copy of the manuscript (not as proof, but for committee members who may want to read your paper to judge its quality).

2. Submitted papers, non peer-reviewed papers. This has some value, as an indication of your recent activity. It is especially useful to the committee if you have few papers (junior researcher) or have not published much recently (so that it is clear you are still active). Again, you may want to join manuscript(s) to your application, or give a link to arXiv if you deposited it there.

3. In preparation, in writing, … There is no clear standard on threshold for what is a paper “in preparation”, so these are usually worthless on a CV. The only exception is if you have very very few (or no) published papers: applying for a PhD position, or early application for post-doc position, with 1 or 2 published papers. Otherwise, my advice is simply not to mention manuscripts you have not finished writing.

First you need to distinguish between publications that have passed the review process (accepted, in press) with those who have not (in prep, in review etc.). The first group are just as published as those that are printed and should/could be listed among the published. The others have not received the accept decision and despite their quality are not yet officially approved by peers and journals. Hence they are equated with manuscripts.

You can divide your manuscripts and papers in as many categories you like in the CV but the bottom line is that those that are not through the peers review will not be counted as highly since no-one yet knows of their deemed quality. But, that said, manuscripts (of all forms) indicates activity so they are not a complete loss in the CV. Unfortunately people have very wide views on what can be included. One person stated that a manuscript existed if it had a title, an abstract, some text and some references. With experiences like that it is perhaps not difficult to imagine that a list of manuscripts in different stages may not count for much other than an indication of activity (no matter the reality).

As for manuscripts in public archives, there will be a middle ground. They obviously exist but have not been peer reviewed. An evaluator should be able to check its quality fairly easily, even if they are not necessarily an expert on the topic. It is also doubtful reviewers search for papers on their own, commonly what they receive to review is what they look at. So the value of such papers is less clear but I would definitely set up a separate category for these sorts of papers in the CV between published peer reviewed and unpublished manuscripts.