Increasingly, it's been hard for me to review articles anonymously because I often know or suspect the identity of the author. In one case, the author had sent me the unpublished ms. a few months before. In another, I recognized the distinctive style and approach. In another, the author had not sufficiently anonymized his article. I was looking for an excuse not to do it anyway so I saw how the writer referred to his own article as his own. In yet another, I recognized the same style and some of the same quotes from another article I had reviewed recently for another journal. I didn't recuse myself because I didn't know the actual name, just that it was the same author. If you used google and really tried to find out who wrote something, you probably could in a lot of cases.
So in smallish subfields anonymity is really hard to maintain. I'd have to really write an article in a diligent way to make it truly anonymous at this point in my own project, so it's not really worth it. I get enough invitations that I have no room in my schedule to send out any other articles. Also, I'd rather only publish in special, monographic issues of journals that are likely to be read.
So basically I know or could find out the identities of many I'm asked to review, and I don't need to go through the process on the other side either.