Most kitchens need a "cooking reference" type cook book, the type of cook book that you can go to and look up cooking times and temps per pound of meat type, or whole wheat bread, or peanut butter cookies, and know that you can find a recipe for it. In my case, I use the (1) Better Homes and Gardens New Cook Book, (4) Mark Bittman's How to Cook Everything: Simple Recipes for Great Food and an old version of The Betty Crocker Cookbook. The Betty Crocker Cookbook was my great-aunts and is full of notes and bits of recipe cutouts from various newspapers and magazines. She was known in our family for her cooking, particularly her fudge. Being the "cook" in our family when she passed on, I was given all of her cookbooks and recipe bits. Bringing family to the table with the same recipes she made in her kitchen means so much to me, and some her recipe scraps are my favorites.
One that I give as an "Finally On My Own" or "New Bride" type gift is (10) Good Housekeeping Step By Step Cookbook. It's perfect for those just learning to cook that need a little more detail and pictures to help show them what to do and how to do it.
Once you get past your reference books, it's all going to depend on your family and your tastes and preferences.
In my case, whenever I'm looking for ideas, I love the (2) Better Homes and Gardens America's Best Loved Community Recipes, Vol I and II. They took the best recipes from church and community cookbooks and compiled them in one place. I have yet to be disappointed with any of the recipes I've tried and they give make ahead tips which are very helpful when planning a menu for parties. I don't believe Volume I is readily available, so if you find it I highly recommend picking it up. I also turn to (3) The Ultimate Southern Living Cookbook quite often, as well as the magazines. My favorite christmas cookie recipes actually came from the Southern Living magazine, and I pull them out every year.
I recommend books that also focus on things you prefer or make often. I live in North Dakota, so I make good use of (6) Williams-Sonoma's Soups for Supper for our long, cold winters. I also love to bake so I have several books focusing on general baking, breads, pies and cookies. My favorite for pies is from Betty's Pies in Duluth, MN and for all around general baking I have used (9) Fannie Farmer's Baking Book frequently.
My final three are also lifestyle type cookbooks. I was a vegetarian for many years, and (5) The Moosewood Cookbook was a constant reference, and still has many favorites. I've lived in several places around the world and have been exposed to a wide variety of foods and flavors and just love the (7) Around The World Cookbook when I'm in the mood for specific cuisine. (8) Weight Watchers Simply The Best is great for healthy, lowfat recipes.
I have many, many, many other cookbooks, but these are my top ten. I do have them in their proper order in a widget along the right side, with their reviews from Amazon.