In addition to the books discussed below, those planning an extended trip to Yellowstone and/or Grand Teton national parks will find an abundance of information in Frommer's Yellowstone & Grand Teton National Parks (Wiley Publishing, Inc.).
Fiction -- Start with some classics: A. B. Guthrie's The Big Sky (Houghton Mifflin, 1947) is now a Montana classic, as is Owen Wister's The Virginian (Macmillan, 1929), set in frontier Wyoming. Then move on to contemporary fiction, like the classic fly-fishing novella A River Runs Through It (University of Chicago Press, 1976) by Norman Maclean. Fool's Crow (Viking Penguin, 1986) by James Welch (a native Montanan) and Heart Mountain (Viking Penguin, 1989) by Gretel Ehrlich are fictional stories that revolve around American Indian and Asian characters. Annie Proulx's Close Range Wyoming Stories (Scribner, 1999) and Bad Dirt: Wyoming Stories 2 (Scribner, 2004) are recent additions by a fine writer who's spent considerable time around Sheridan. Poet James Glavin's beautifully written The Meadow (Henry Holt, 1992) is set in the Tie Siding area of southeast Wyoming.
Montana is fortunate to have the best of its literature compiled in one volume, The Last Best Place (University of Montana Press, 1988), the definitive anthology of Montana writings, from American Indian myths to contemporary short stories.
Nonfiction -- Novelist Ivan Doig wrote a beautiful memoir about his youth in Montana, This House of Sky (Harcourt Brace Jovanovich, 1978). Gretel Ehrlich's The Solace of Open Spaces (Viking Penguin, 1986) is a beautifully written, evocative account of Wyoming ranch life. Paul Schullery's Searching for Yellowstone (Mariner Books, 1997) is a great look at the ecology of the world's first national park and mankind's impact on it. Eric Sorg's Buffalo Bill: Myth and Reality is an informative read about the man who truly defined the mythos of the West.
If your interests lean more toward geography, check out the Roadside Geology of Montana (Mountain Press, 1986) by David Alt and Donald W. Hyndman, and the similar Roadside Geology of Wyoming (Mountain Press, 1988) by David R. Largeson and Darwin R. Spearing.
History -- Perhaps the best, and easiest, read about the history and culture of Montana is found between the covers of Montana, High, Wide and Handsome (University of Nebraska Press, 1983), written by Joseph Howard and first published in 1944. Another interesting historical tome is Aubrey Haines' two-volume The Yellowstone Story (University Press of Colorado, 1977).
Films
Hollywood adapted Norman Maclean's A River Runs Through It in 1992 with Brad Pitt; Rancho Deluxe (1975) is set in Livingston, Montana, and depicts a rapidly changing place though cattle rustlers played by Jeff Bridges and Sam Waterston; Little Big Man (1970) is a revisionist Western that covers Custer's Last Stand and much more. Wyoming films of note include the made-for-HBO The Laramie Project (2001), an adaptation of a stage play about the murder of gay college student Matthew Shepard, and Close Encounters of the Third Kind (1977), Steven Spielberg's UFO epic that climaxes at Devils Tower National Monument.