Cut eggs in half lengthwise. Remove yolks. With fork, mash yolks; add mayonnaise, mustard, salt and pepper.
Divide amount in half. To each half, add the ingredients for one of the variations below.
Refill whites with yolk mixture and garnish as directed. Serve immediately or store, covered, in refrigerator. Use within 3 days.
To take deviled eggs to a picnic, put the cooked egg white halves in a plastic container and the devilled yolk filling in a plastic bag. Place both in the cooler. When you are ready to serve, cut off one corner of the plastic bag and pipe the filling into the egg white halves.
For distinctive deviled eggs, mix egg yolks with some chicken salad and stuff this mixture into the egg whites.