Oh...don't get me started. I've been both cooking and working in bookstores for 30 years!
From a home cook:
On Food and Cooking--McGee
The Flavor Bible--Page
Joy of Cooking-most people hate the 1997 revision. I'm less disappointed in it but previous editions and the 75th Anniversary eds are a better bet. General but shockingly comprehensive.
Cook's Illustrated Cookbook--painstaking recipe writing
Vegetarian Cooking for Everyone (or New Vegetarian Cooking for Everyone) by Deborah Madison
Simple Food I--Alice Waters
James Peterson--just about anything
Madelyn Kamman--The New Making of a Cook
La Varenne Practique--Ann Willen
Jacques Pepin--His older technique book is great, I understand, but his Essential Pepin comes with a searchable DVD
Roasting by Molly Stevens
Braising by Molly Stevens
--Chinese--Grace Young, Barbara Tropp
--Middle Eastern/Mediterranean/North African:
Claudia Roden's New Book of Middle Eastern Food.
Anything by Paula Wolfert
Zahav by Michael Solomonov
--Other Latin American:
Cocina Latina by Maricel Presilla
The South American Table by Maria Kijac
Peru: The Cookbook by Acurio
People like Lydia Bastananich a lot but I am a diehard Marcella Hazan fan. Older. Not as lushly produced. Not glossy. The real deal presented over the course of a number of cookbooks.
--Greek--Anything by Diane Kochilas (also--see her website.)
--Russian/former Soviet Union countries:
Please to the Table by Anya von Bremzen
Mamushka by Hercules (also covers Ukraine)
Joan Nathan--many Jewish-American cookbooks
Olive Trees and Honey by Marks--Jewish-vegetarian cooking from across the diaspora
--Japanese--Japanese Cooking: A Simple Art by Tsuji
Madhur Jaffrey, Yamuna Devi,
How to Cook Indian--Kapoor
I like James Peterson's New French Food
Richard Olney's Simple French Food is a classic
Patricia Wells--many over a long career.
There are many people here on CT who have much more expertise here than I when it comes to classic French cooking.
Yeast Breads--Peter Reinhart--Breadbaker's Apprentice or Crust and Crumb
Cake--Rose Levy Barenbaum--The Cake Bible
Pastry-Pies, etc--Bernard Clayton or Rose Levy Barenbaum
French Pastry is beyond my expertise or, even, my will. That is what bakeries are for.
General Desserts-- Dorie Greenspan, David Lebovitz, Alice Medrich. Old school but still good--Maida Heatter
Ice Cream--David Lebovitz--The Perfect Scoop
Korean--I've got a few but none I'm crazy about. However, Koreatown: A Cookbook is about to make me break my "NO NEW COOKBOOKS" moratorium
Thai--I still use an old book from the 80's called The Original Thai Cookbook by Brennan. No frills but the 1st one in the States that didn't dumb down ingredients. I think it's out of print.
American Southern--skip Paula Deen and look for Edna Lewis, Sean Brock--I'm sure there are others. It's not my favorite cuisine. Edward Lee's Smoke and Pickles cookbook is an amazing mashup from a Brooklyn Born, Korean-American who now cooks in the south. Teaches you how to hack an indoor, stovetop smoker.
Fermentation--Sandor Katz's Art of Fermentation is the bible.
Pickling-Joy of Picking (Zedrich) and Asian Pickles by Solomon--both good