The Grapes of Wrath is the best example of a novel exploring the Great Depression, but Steinbeck's Of Mice and Men is set in the same time period. A novel that explores the American culture in the lead-up to the Great Depression would be Babbit by Sinclair Lewis.
An under-rated novel from the Great Depression era is The Day of the Locust, a short novel by Nathanael West. This is a great book with plenty of social commentary.
Besides Steinbeck's magnum opus The Grapes of Wrath, there is also his novella which preceded this work: Of Mice and Men. This short work, too, tells of the plight of man as an itinerant worker during the Great Depression. Then, there is John Dos Passos's The U.S.A. Trilogy, a major work that considers the first three decades of the twentieth century. relating the lives of twelve different characters, along with newsreels and private moments of the author himself. This is truly a cleverly written novel.
John Steinbeck's The Grapes of Wrathis the quintessential American novel about the Great Depression. We not only follow one fictional family, the Joads, but we also experience the bigger picture across the country through the intercalary chapters. In this novel, we see all aspects of the time: the displaced, the farmers, the businessmen, the landowners, and more.
One other novel to note is The Great Gatsby, whose post-Depression setting shows the grand contrast between the having nothing of the Depression and the excesses and abuses of the time just after the dearth and hardship.
To Kill a Mockingbird is also considered fiction, although it is based on the author's original life experiences. The life of the townspeople (particularly the children as demonstrated by the class experiences) and the Negro population certainly demonstrate the Great Depression. Doctor and lawyers agreeing to take their pay in increments of food most certainly demonstrates Depression era bartering.
One other book that very famously deals with conditions in the Great Depression is Of Mice and Men. This is another Steinbeck book that examines the problems faced by poor agricultural workers during the Depression.
Also, you might look at The Bread Winner, by Arvella Whitmore. It is much more of juvenile fiction that Steinbeck's book. It deals with a young girl whose family becomes poor and has to move into a slum during the Depression.
Three great books that immediately come to mind when I think of the Great Depression are the following. Firstly, a great book is Bud, not Buddy, which charts the quest of one young boy to try and find his father and the strange people that he meets and the situations that he faces on the way. This is all set against the backdrop of the Great Depression and also explores the role of Jazz music an its popularity at this time.
Secondly, the classic work of fiction regarding the Great Depression is Steinbeck's masterful The Grapes of Wrath, which follows the Joad family as they move across the country in search of work, and the misery, povery and challenges that they face as a result. This is a truly moving account that also explores the way that migrant workers were exploited in so many different ways.
Lastly, although this is a non-fiction book, it still gives a very interesting account of the Great Depression. Seabiscuit: an American Legend is the fascinating story of how this horse came to be a symbol for the poor and downtrodden during this time of history.
I have included the links to the enotes study guides on these books below. Another one I have recently finished reading is Water for Elephants, which looks at the life of a travelling circus during the Great Depression.