I got rid of most of my cookbooks before we moved earlier this year. I'm left with:
The Joy of Cooking: It's my second copy. A go-to for basic recipes and instruction, and inspiration. My daughter likes to read cookbooks, so I often have to ask her to fetch it from her room when I need it.
America's Test Kitchen Quick Family Cookbook, or something like that. This is a new one and it's great. Great recipes, and lots of good technique and ingredient discussion.
A small binder full of family recipes. We only use 4 or 5 of the recipes, but because my mom compiled it and everyone contributed, it's worth hanging on to.
Winston-Sonoma: Bread. It's one of those thin books from the series. Lots of good recipes for making day-to-day bread. Sandwich bread, English muffins, cornbread, etc.
Claire's Italian Feast. A local-ish restaurant well-known for it's vegetarian food. I use it less for direct recipes and more for inspiration.
Alton Brown, I'm Just Here for the Food. Not a cookbook per se, but a food science and technique book mostly about cooking meat, with some recipes included.
Other than that, I have a clipboard that I use to hold printed Internet recipes and I get a lot of food books (recipes, nutrition, food politics, etc.) from the library.
If I REALLY wanted to pare down to just one, I'd keep the family binder and just Google the rest. But since they take up about one foot of shelf space (which is about a tenth of what I used to have), I think I'm good. :)