AK Press: While clearly not an academic press, and often focusing more on cookbooks than animal studies, AK Press still turns out books dedicated to a radical animal studies.
Columbia University Press: Has published several key books in Animal Studies, and obviously continues to publish more. Wendy Lochner seems to be the editor for animal studies.
Lantern Books: While not a press that is specifically academic, it has several important works, and keeps publishing important works, in animal studies.
University of Minnesota Press: Has the Posthumanities series, edited by Cary Wolfe. While not dedicated specifically to just animal studies, animal studies is obviously an important and frequent subset of the books that come out of this series.
Palgrave Macmillan has a the Animal Ethics series, edited by Andrew Linzey and Priscilla Cohn.
Penn State University Press has the new Animalibus: Of Animals and Cultures series, edited by Nigel Rothfels and Garry Marvin. I had a chance to briefly talk to Nigel about this series at The Non-Human Turn conference, and he said the hope was to publish books that were about something in particular, rather than a purely philosophical of theoretical treatise.
Reaktion Books has the unique Animal series, edited by Jonathan Burt.
Honorable Mention (these are presses that frequently, and currently, keep publishing heavily in animal studies, without having a dedicated series or editor):
University of Chicago Press
Fordham University Press
Oxford University Press
So, what did I miss?