Measuring spoons: Go for a set on a ring that includes at least ¼, ½, and 1 teaspoon and ½ and 1 tablespoon.
Measuring cups: You'll need one for liquids (at least a 2-cup capacity) and a set of at least four (1 cup, ½ cup, ⅓ cup and ¼ cup) for dry ingredients. Don't be tempted to use the dry ones for liquid ingredients or you'll risk ruining your creation with mismeasured ingredients.
Mixing bowls: Make sure you have several of different sizes and get at least one with a pour spout so you can fill muffin cups and make pancakes without dirtying another utensil. (Fewer dirty utensils = less cleanup!)
Long-handled wooden spoons: For making brownie batter, mixing chocolate chips into cookie dough or stirring up some creamy filling. (Also good for licking when you're done stirring!)
Rubber spatula: This is essential for getting every last bit of that batter into the pan ... or into your mouth (as long as it's eggless). Also great for spreading frosting.
Whisks: You probably only need one, so make it a good, sturdy one with plenty of wires. You'll use it to keep your custard from getting lumpy, when you want to whip some cream to top your pie and when the recipe says "two eggs, gently beaten."
Rolling pin: For rolling out dough, not chasing your spouse!
Electric mixer: A simple handheld electric mixer that has at least three speed variations will save your arm when you need to mix batter or whip cream.
Baking pan: 9 x 13 or 8 ½ x 11 sizes are the most popular, but an 8- or 9-inch square pan is also useful ... especially if your family likes brownies!
Flat cookie sheet: Use for pizzas, rolls, biscuits and, of course, cookies.
Baking sheet with a rim: For making jelly rolls or dessert bars, but more importantly, for baking chicken or veggie nuggets, so they don't slide off the pan. (Don't be fooled into using these for your cookies—they won't bake evenly.)
Muffin pan: In a house with kids, you can barely make it a month without an official muffin- and cupcake-maker. Buying a silicone one will eliminate the need for cupcake liners, but the sturdy metal ones work great and last forever. Consider getting different sizes (mini, regular or jumbo) depending on your family's muffin-size preferences.
Round cake pans: You'll need at least two if you plan on making any layer cakes.
A glass pie plate: Of course you can use this for the traditional apple, cherry and pumpkin numbers, but it's also good for pot pies, small casseroles and quick breads.
Oven mitts: Look for the glove variety and check the thickness of the padding to make sure it'll provide you plenty of insulation. A pair of animal-head oven mitts will pull double duty as puppets to keep the kids happy in the kitchen.
Thin, flat metal spatula: This is essential for removing cookies from a baking sheet without destroying them. (The ruined ones taste just as good, they're just not good for company.)
Oven: (But you knew that. You did know that, right?)