Go West, Young Man! (books about the frontier)
As Dana says, definitely Willa Cather.
Little House books
Conrad Richter's Awakening Land trilogy and The Light in the Forest
Last of the Mohicans (Much better than Mark Twain says)
Mark Twain's Life on the Mississippi
Hamlin Garland's short stories in Main-Travelled Roads
The Virginian, Owen Wister
Shane, Jack Schaefer
Riders of the Purple Sage Zane Grey
The Octopus, Frank Norris (depressing, but not as depressing as his McTeague, one of the most depressing novels of all time)
Bret Harte's short stories
The Call of the Wild, White Fang Jack London
The seminal essay on the role of the frontier is Frederick Jackson Turner's "The Significance of the Frontier In American History," which is the first chapter of his book i The Frontier in American History, which is widely available online. Henry Nash Smith's Virgin Land: The American West as Symbol and Myth is very readable.