How appropriate or common is it to recommend referees for your paper?
It's fairly common for journals to ask for reviewer recommendations. This is to help them get reviewers. Suggested reviewers make the editor's job easier, since they no longer need to work that hard to find people who can review the paper.
The downside isn't that it's unethical - I don't see why it would be - but rather that the authors are going to suggest their friends or even commit peer review fraud by nominating themselves. But that's something for the editor to worry about, not you.
Finally it's worth noting that not all reviewers you recommend will be invited to review your article - it's fairly common for journals to have a "one recommended, one self-invited" policy for example. In fact, it's possible none of the reviewers you recommend are invited.
A significant number of physics journals require authors to recommend referees. So it is common to recommend referees.
I do not believe that recommending referees is unethical. It is the editor that picks the referees, not the recommending author. If the editor picks the author's recommendations without considering the quality of those referees, the editor is behaving unethically.
Some editors will exclude referees suggested by the authors.
A small addendum to @Allure's and @AnonymousPhysicist's answer. The "one recommended, one self-invited" policy is based on two ideas:
- the authors have a good idea of the experts in the field, and can do a good job identifying people who will give a knowledgeable review;
- ... but reviewers recommended by the authors may be biased toward them.
So making sure that the reviewers are a mix of recommended and non-recommended is wise editorial policy. However, this means that recommending a long list of everyone who you can think of is a bad idea, as it means that at most one of those people will be invited to review.
But yes, if you are asked to recommend reviewers, doing so is (1) ethical, (2) in your interest, and (3) doing the editors a favour (because they don't have to work as hard to identify suitable reviewers). (You can say, "I shouldn't have to do this, it's their job", but why shouldn't they benefit from your knowledge of the field? How hard is it for you to list a couple of researchers in your field who you think are well-informed on the subject?)
Also worth noting that reviewers are usually required to certify that they don't have a conflict of interest (COI: typically includes blood relatives; current or former academic supervisors; and people who have co-authored or worked together on a grant within some time window). This automatically rules out some of the most positively biased reviewers (and don't bother recommending reviewers in these categories, it will just waste everyone's time).