Should paper reviews be signed? Occasionally, in an otherwise-anonymous paper review, the reviewer will voluntarily sign their name, revealing their identity to the author.

Should reviewers do this, and under which circumstances?

(For the purposes of this question, assume that the reviewer knows the author's name - that is, the review process is not double-blinded.)
I do not think the "should" word is appropriate here. Each reviewer decides whether he/she wants to sign it or not. Most reviews today are anonymous. I think it is considered sort of default by the journals today. One might tend to think that a signed review will more fair. But a decent person will do a fair review regardless of whether he/she signs it or not. When a review is signed, this could result in some unexpected complications: suppose a reviewer did not understood one of your analyses. So, once the review is signed, the author might write directly to the reviewer, without involving the editor. This might violate the review process. I also do not think that most of the reviewers are interested in such sort of communication.