I have three who I am very impressed by. Ansel Adams, of course.
I pretty much got my start many years ago by trying to emulate the late Josef Scalea who was a newspaper photographer with the Seattle Times. (Some shots remain available at http://www.seattlegallery.com/)
But, I really learned a lot from working side by side with a PJ in Japan named Michael Stanley. (http://www.mejstanley.com/) His work in so many different areas is remarkable.
Many of the photographers I enjoy have already been mentioned... but I'll try to add two others, radically different in what they did, but both of great artistic interest to me.
I've always enjoyed the portraiture of Yousef Karsh. His work of Churchill is very well known, but also see his portraits of Earl Warren, Albert Schweitzer, the Rev. Martin Luther King, Jr., or Boris Karloff. Karsh may not be part of the current avant-garde of the photographic world, but his portraits of some of the great men and women of the twentieth century are in some ways the definitive memory of those people for many.
For sheer imaginative vision when the photos were taken, one needs to look at the work of Man Ray. Man Ray was a part of the Dada and Surrealist movements, which, quaint as some of the work appears today, were ground-shaking in their time.
These are a few living photographers whose work and/or attitude toward their photography that I like: Ralph Gibson, Cindy Sherman, Jill Greenberg, Timothy Greenfield-Sanders, Nenad Bojic, Jerry Uelsmann, Elliot Erwitt, Rick Waldroup, Sally Mann, Duane Michaels, RFC, Susan Meiselas, Zeke Berman and many others that I cannot think of their names right now. If you think they are diverse, you should see my picks for dead photographers!