To those scientists who haven't served as editors or associate editors of scientific journals, I can assure you that it's already too hard to find enough qualified reviewers willing to do the job without threatening them with exposure as well! So, if you want your papers to be published within a reasonable timeframe, you'll pretty much have to put up with anonymous reviews.
I've been an associate editor of Geochimica et Cosmochimica Acta for 11 years and an Editorial Board member of Chemical Geology for 4. I think anonymous reviews are perfectly acceptable, but that the editor evaluating the reviews should always be identified, both to the authors and in the published manuscript. Reviewers should be permitted to request anonymity, but authors should always be instructed to specifically acknowledge in their manuscripts the contributions of those reviewers who do not request anonymity. This, in fact, might encourage more reviewers to identify themselves. I don't know about you, but it tickles me pink when I see my name in print!