These are the cookbooks that I think should be the foundation of any kitchen. Those who don't eat meat: hang on for the special vegan section at the end
1. The Way to Cook by Julia Child. I have Mastering the Art of French Cooking, and it's marvelous, but this is the book I open most often. This is the guide to cooking the things almost everyone wants to make, perfectly.
2. Essentials of Classic Italian Cooking by Marcella Hazan. There are newer, hipper Italian cookbooks out there, but when all's said and done, I turn back to Marcella. There's something about her seventies sensibility that I actually find very soothing; her recipes are neither showy, nor designed to be made in ten minutes between IPO teleconferences.
3. I'm Just Here for the Food and I'm Just here for More Food by Alton Brown. Oddly enough, I don't particularly care for most of his recipes. So why do I own both of his books, and recommend them to everyone? Because Alton Brown explains food better than anyone. His books go over the chemistry and explain the concept of what you're trying to do, which equips you to go out and deploy (or modify) your own favorite recipes more successfully. One small example: he's the reason I bought an electric griddle to cook pancakes at exactly 350 degrees, which produces a perfect pancake every time.
4. Fast Food My Way and More Fast Food My Way by Jacques Pepin I cannot overstate the excellence of these books. They stand alone in the genre of "Things I can make quickly after a long day of work". Most 30 minute meals are designed to be consumed in front of a television in five, and could as easily replaced by triscuits and low-fat Alouette with a Pop-Tart chaser. Jacques Pepin's recipes are not merely things you can make, but things you should make, and will make even when you have time to kill.
5. The Betty Crocker 1950 Picture Cookbook is not merely a fine bit of kitsch. It is actually a pretty reliable guide to cooking American staples, from meatloaf to macaroni and cheese. My mother, who turned herself into a pretty reliable gourmet by way of classes with folks like John Clancy and Craig Claiborne, and actually did a stint as a caterer, cooks a surprising number of meals out of this book. It's ordinary American cooking, really well done, from an era before salad oil replaced butter, and health replaced flavor.
6. The Gourmet magazine cookbook I've never been able to get into The Joy of Cooking; somehow, it's sensibility of comfortable shoes and stuffing olives into the gaping maw of Midwestern ennui oppresses me. The Gourmet Magazine cookbook fills the role in my cupboard that Joy fills for many other folks: there's a recipe for damn near everything. And I haven't found a bad one yet.
7. Julia's Kitchen Wisdom by Julia Child This is an odd little book; it's basically her tips and tricks in the kitchen. But it's invaluable. From who else would you learn to simmer rice in a tomato soup, and then puree, to get cream of tomato soup without the fat? Or hardboil an egg absolutely perfectly, every time? I especially recommend it for the new cook, but almost everyone will learn something.
8. The Union Square Cafe Cookbook and Second Helpings from the Union Square Cafe by Danny Meyer These are my hip, new millenium, granite-counters-and-stainless-steel-appliances books from the owner of my favorite restaurant in New York.
9. How to Cook Everything by Mark Bittman The New York Times food writer is an absolutely gorgeous cook, and I can't recommend his books highly enough. Like the Gourmet cookbook, it covers enormous ground, but with more explanation as it goes, and usually, much simpler recipes. And like the Gourmet cookbook, I haven't yet made something I didn't like.
As you can see, I'm basically a Europe/American focused gal; I don't do a lot of Asian or Indian, though I'm hoping to learn this year. Readers who do know those cuisines are heartily invited to offer suggestions in the comments
For Vegans, or people trying to use fewer animal products:
Vegan with a Vengeance and Veganomicon by Isa Chandra Moskowitz. These are, by far, the most fun vegan cookbooks I own. The recipes really are delicious, easily enough to recommend them to non-vegans. I've made brunch for non-vegans a ton of times who never recognized that they were having a vegan meal.
The Joy of Vegan Baking Indispensible. Vegan baking is tricky--it turns out eggs are really, really useful. This book explains what it's doing and why, and incidentally, produces some pretty amazing desserts. The tofu chocolate mousse is the fastest, easiest, most elegant dessert you can whip up on absolutely no notice.
How to Cook Everything Vegetarian by Mark Bittman If anything, even better than the original omnivore book. Not all the recipes in here are vegan, but many are, and they're clearly marked. A number of others are veganizeable. But really, don't think of this as a book for vegetarians; it's a book for everyone who eats vegetables.
Books that aren't really cookbooks, but about food:
Appetite for Life It's the biography of Julia Child. 'Nuf said. Don't miss it.
Miriam's Kitchen: A Memoir by Elizabeth Erlich This is a really beautifully done book about a woman, her mother-in-law, and how she and her husband gradually moved back into keeping kosher.
The Omnivore's Dilemma by Michael Pollan There is much to be annoyed about in Pollan's brand of smug coastal foodyness. But the book itself is the clearest map I've yet found of exactly how our food chain works in America.
The Gallery of Regrettable Food and Gastroanomalies by James Lileks. Most humor books don't make me laugh. These produced a laugh-out-loud moment every few pages. Basically, Lileks takes horrible recipes from those old cookbooks lying around everyone's attics, the kind of recipes that make you wonder whether the average American in 1950 lived entirely on Spam, ketchup, and lard. Worth every penny you spend on them.
Salt: a World History by Mark Kurlansky It's a book about . . . salt. Salt, it turns out, is incredibly cool. No, seriously, I can't explain it; just buy it. You will not believe you could be so fascinated by the stuff you just sprinkled on your steak.