Since you can now easily google to find thousands of pages discussing the anthropic principle, there seems little point in producing an extensive list of links. So I've curtailed this page to the following brief suggestions:
The physics Los Alamos preprint archive is a good place to search for the latest physics-related papers, including ones dealing with matters anthropic: http://arxiv.org/.
The "Arxiv", however, does not cover a great many relevant contributions that come from outside physics---especially philosophy. To find these, if you have access to a university's subscription database, try The Philosopher's Index (and perhaps Web of Science).
Since in my opinion (and as I tried to illustrate in my book), there are a number of topics that share the same essential problems of observation selection effects, and since some of these are mainly discussed by philosophers and others by physicists, and since many avoidable mistakes arise from ignoring some of the constraints that become obvious once one considers the whole range of contexts in which anthropic issues crop up, I urge the serious student of the field to familiarize themself with relevant writings of both philosophers AND physicists (as well as those of computer scientists, statisticians, biologists, and theologians, and game theorists).
The Preprints archive on this site links directly to many of the major papers.
I maintain another website specifically on the simulation argument, which is one significant application of anthropic reasoning. I also have a homepage.