New Orleans Book List - Fiction
1. A Confederacy of Dunces by John Kennedy Toole
If you want to embrace your inner Yat, Ignatius is the character who will help you on your way. Toole's novel is New Orleans from the 1960s, before cable TV homonegized live.
2. Sandrine's Letter to Tomorrow by Dedra Johnson
The time frame jumps to the 70s in Dedra's first novel. Sandrine is a light-skinned black girl growing up in New Orleans. This book should be on Oprah. No kidding.
3. Gumbo Ya-Ya by Lyle Saxon
This is a great anthology of Louisiana folk tales. Great way to get a feel for the stories we all grew up with down here.
4. New Orleans Stories edited by John Miller
A great anthology with stories from Whitman, Faulkner, Rice, Capote, Percy, Williams, Hurston, and an introduction by Andrei Codrescu.
5. Sunset Limited by James Lee Burke
All of Burke's "Dave Robicheaux" novels rate being here. This one is just representative of them all
6. Interview with a Vampire by Anne Rice.
This is a must-read in terms of New Orleans fiction. Whether you continue from there with the rest of Rice's vampire novels is up to you.
7. The Witching Hour, and Lasher by Anne Rice
Rice's "other" New Orleans series, the Mayfair Witches. The Witching Hour is set in the Garden District, and Lasher continues where TWH leaves off. There's one chapter in Lasher where Rice describes one of the family matriarchs, who is in her 70s, walking from her house at St. Charles Ave. and Amelia St., down St. Charles to the other Mayfair house on First Street. It's one of the most vivid descriptions of uptown New Orleans in print. Even you don't like the story, go check Lasher out at the library and read this scene.
8. The Feast of All Saints by Anne Rice
Rice's take on the gens de couleur libres in antebellum New Orleans.
9. The Voodoo Queen by Robert Tallant
A well-written (albeit very romanticized) version of the life of "voodoo queen" Marie Laveau.
10. Exquisite Corpse by Poppy Z. Brite (amazon link because Powells doesn't have a cover photo)
Serial killers, cannibalism, and other horror fun, set in Da Quarters. Neat stuff!
11. Liquor: A Novel by Poppy Z Brite
A neat tale set in a New Orleans restaurant. A lot of docbrite's fans slammed Liquor when it came out, but I enjoyed it.
12. The Awakening by Kate Chopin
If you haven't already had to read it for a class, this is a great story of a woman's struggle with marriage in the 1800s.
13. New Orleans Sketches by William Faulkner, edited by Carvel Collins
A collection of short prose by Faulkner, originally published in Da Paper in 1925.14. Cane River and Red River by Lalita Tademy
Strictly speaking, these aren't New Orleans stories, but Cane River in particular ties directly to the city, since any tale of a plantation upstate (Natchitoches, LA, is on the Cane River) ties back to the city. Red River continues the story post-Civil War, in Colfax, LA. Great reads about African Americans in Louisiana in the 1800s.
OK, I know I'm forgetting more than I'm remembering here, so I'll stop at this point and let y'all add more in comments.
UPDATES:15. Jitterbug Perfume by Tom Robbins
16. The Moviegoer by Walker Percy
17. Lives of the Saints by Nancy Lemann
and some suggestions from the LiveJournal neworleans community:
18. Coming Through Slaughter by Michael Ondaatje (about Buddy Bolden and E. J. Bellocq
19. The Axeman's Jazz: A Skip Langdon Novel by Julie Smith. Smith has a number of mysteries with her Skip Langdon character.
20. Off Magazine Street by Ronald Everett Capps. This is the book that the Travolta film, "Love Song for Bobby Long" was based on.
21. Chita: A Memory of Last Island by Lafcadio Hearn. More Louisiana than New Orleans, but it captures antebellum Louisiana nicely.
also these suggestions:
Anything by Patty Friedmann, but particularly Eleanor Rushing, Side Effects, and A Little Bit Ruined (her post-K novel).
Anything by Sheila Bosworth, but particularly Almost Innocent.
Anything by Christine Wiltz.
For mystery fans: J.M. Redmann's Micky Knight series.

Ellen Gilchrist, In the Land of Dreamy Dreams
Thanks for the list! I'm reading Sandrine right now and can hardly put it down. I agree with Ray, more books like this!
Don't forget David Fulmer's Valentin St Cyr mysteries:
Chasing the Devil's Tail
Jass
Rampart Street
No freaking way. I’m absolutely disagreeing. Next time when you post something think about reaction of readers.
Humph, you've changed my mind! Your arguments are convincing indeed. Despite I'm not a person who is easy to be convinced.