Shell hard-cooked eggs and halve them lengthwise. Gently loosen the yolk and remove it, taking care not to break the white. Mash the yolks with a fork or, if there are many, process them in a blender or food processor.
For each yolk, add 1 1/2 teaspoons of one of the following: mayonnaise, sour cream, French dressing, or softened butter mixed with a little vinegar. Blend to a smooth paste. Season with salt, pepper, and dry or prepared mustard. If you prefer spicier eggs, add one or more of the following to taste: curry powder, Worcestershire sauce, cayenne, or hot-pepper sauce.
For variety, try minced seafood, ham, onions, herbs, or anchovy paste.
Use a teaspoon or a pastry tube to fill the whites with the mixture. Top with a sprig of parsley or dill, sliced pimento or olives, caviar, or paprika. Cover loosely with damp paper towels and chill 1 hour before serving.