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.