Here's a list of some good readings on anthropology and religion. The ones with * I'd especially recommend- not necessarily for the completeness of them (in fact, most are rather specific ethnographies) but rather because I just thought they were stellar reading and (dare I say) enjoyable.
*Anderson, E. N. Ecologies of the Heart (Nice and broad-sweeping- one of the few I find that gets at a lot of issues, ranging from medicine to environmental ethics combined with cognitive issues.)
Atran, Scott. In Gods We Trust
Bourdieu, Pierre. Outline of a Theory of Practice
Durkheim, Emile. The Elementary Forms of Religious Life
Feld, Steven and Keith Basso. Senses of Place
Frake, Charles. Language and Cultural Description. (Arranged like a series of articles, has some good ones and Frake was a brilliant cognitive scientist. However, kind of dry reading if you're not really into it and the last I checked the book is out of print and expensive to get a used copy.)
Goulet, Jean-Guy. Ways of Knowing.
Hostetler. Amish Society.
* James, William. The Varieties of Religious Experience. (Still one of the best out there.)
Kuhn, Thomas. The Structure of Scientific Revolutions.
* Lansing. Priests and Programmers (A good ethnography that shows how ecological and social sustainability can be grounded in more formalized, larger scale religions with priests- and also why the colonists just didn't "get" it.)
* Lehmann, Artur C., James Myers, and Pamela A. Moro (eds.). Magic, Witchcraft, and Religion: An Anthropological Study of the Supernatural. (The only decent reader I've found. It's an introductory reader, so it's sort of user friendly- but it isn't a good textbook- not found one yet. As a reader, though, it's quite good and it's worth it for the bibliography.)
Malinowski, Bronislaw. Magic, Science and Religion.
Marx, Karl. Elster, Jon (ed.): Karl Marx: A Reader. (Marx had some good ideas on religion. There's been some good spin-offs and refinements of Marx's theories since- tons of Marxists. Gramsci is particularly interesting, if cryptic since he wrote some of his stuff from jail.)
Mauss, Marcel. Magic.
* Milton, Kay. Loving Nature. (Aside from some decent, though sometimes problematic, treatment of environmental politics in the modern first world, her treatment of magic, science, and religion and the human tendency to assign person-hood to things is great.)
* Nelson, Richard. Make Prayers to the Raven. (If you're going to read just one specific little ethnography, I'd recommend this one. It's a joy to read, gives a very in-depth treatment of the culture's religion and its tie to ecological sustainability, and gives a good inside look at an animistic worldview.)
Rappaport, Roy. Pigs for the Ancestors (The classic ethnography about ecological sustainability and religion. He wrote another book as well: Ritual and Religion in the Making of Humanity.)
Tremlin, Todd. Minds and Gods: The Cognitive Foundations of Religion (I'm throwing this in here- it's on my reading list but I haven't gotten to it yet. Sounds interesting.)
Weber, Max. The Protestant Ethic and the Spirit of Capitalism.
Young and Garro. Medical Choice in a Mexican Village.
Good general histories and summaries of the major anthro theorists:
Barnard, Alan. History and Theory in Anthropology. (Not basic, but good.)
Barrett, Stanley. Anthropology: A Student's Guide to Theory and Method (Very basic. But, that's the nice thing about it.)
McGee, R. Jon and Richard Warms. Anthropological Theory: An Introductory History. (Another not basic but good one. Unfortunately, exorbinantly priced too. I'd recommend Barnard's over this one in part because of the price differential of $60+.)