Here are the cookbooks I can't do without, and some that are great for certain purposes.
Vegan with a Vengeance by Isa Chandra Moskowitz
This was my first vegan cookbook and I've never been disappointed by anything I've made out of it.
The Ethnic Vegetarian: Traditional and Modern Resources from Africa, America, and the Carribean by Angela Shelf Medearis
An incredible resource. Traditional African, Native American, Creole and Cajun, Southern and Caribbean recipes, either originally vegetarian or seamlessly adapted.
Vegan Soul Kitchen by Bryant Terry
As a Southerner, this cookbook was a major discovery. His citrus collard greens recipe is amazing, and I can't wait to cook my way through it.
Viva Vegan! by Terry Hope Romero
I lived in Mexico as an exchange student when I was 16, and my love for latin food, particularly that of Southern Mexico, is limitless. This cookbook is muy sabroso.
Vegan Brunch by Isa Chandra Moskowitz
I am vegan and brunch is my favorite meal. Ergo, this book. I used to host a big, potluck brunch for friends at my house (I aimed for once a month... but you know how things are). When I get settled in somewhere, I'm definitely going to start that up again.
Mastering the Art of French Cooking by Julia Child, Simone Beck, and Luisette Bertholle
Absolutely foundational for technique, flavor combinations, and tools, etc. No one calms you down when something is going badly like Julia does.
The Candle Cafe Cookbook by Joy Pierson, Bart Potenza, and Barbara Scott-Goodman
From the people behind what is possibly the most successful vegan restaurant in the country, Candle 79 in New York. The Candle Cafe came first, and this cookbook is full of great, functional recipes (by functional, I mean that there is not an aspic in sight, and lots of things you can make in a reasonable amount of time to serve to guests or just for dinner).
Veganomicon: The Ultimate Vegan Cookbook by Isa Chandra Moskowitz and Terry Hope Romero
The Native Foods Restaurant Cookbook by Tanya Petrovna
I've had some major successes and one or two failures out of this cookbook, but overall, I'm really glad I found it.