Should one keep record of papers one reviews? (and of the reviews themselves) Just like my other research-related activities, I keep a complete record of the reviews I perform: both the original papers and the reviews I have written, as well as the revised manuscript I receive one, and the final published manuscript if it is published (but sometimes in a different journal!)

I don't think I ever read anything in reviewer guidelines that forbid this, but I recently met someöne who argued that confidential material should be deleted after review. It's true that keeping it on my hard drive exposes it slightly to a risk of breach of confidentiality, but no more than the rest of confidential material that I handle every day…

So, what are policies on this matter and what are the existing practices?
I do the same (i.e., save all versions of a manuscript I receive and all of my and the other reviewers' comments that I receive through the review process). I save them in a single directory according to their manuscript number, which tends to keep things fairly organized and easy to find later.

Why might I want to find them later? First, when I receive a revision, I find it is a lot easier to go back and look at the files I have stored locally to see what I recommended change (in case it has been months since I first saw the manuscript), whether the author(s) did, in fact, change anything, and whether the changes were actually in-line with my and the other reviewers' suggestions. This came up recently when I received a revision that claimed to make changes but I found they had actually not made changes in the manuscript (the original and revision were strikingly similar) and I suggested a rejection.

The second instance where this can come up is receiving the same manuscript from a different journal (e.g., because it was rejected by the journal you reviewed for first). Having your previous comments and the previous version allows you to see how the manuscript has developed and either provide original feedback or reiterate points that still need improvement that you highlighted in your previous review. Or, decline to review because youf ind it difficult to present an unbiased opinion.

A third, and final, reason that I find it useful to save these things is pedagogical. In graduate school, several professors sent us versions of their reviews for manuscripts so that we could see how to write a peer review. Having manuscripts and your reviews available makes passing down that future pedagogical activity much easier. (Note that sharing manuscripts may be more controversial than sharing one's review, but if the paper was previously available as a working paper or conference paper and was subsequently published, I see little ethical concern with sharing the manuscript with future students.)