Eggs can be stored for at least 1 month, covered in the refrigerator. Freezing is often unnecessary, but it can be done.

[edit] Steps

Select fresh eggs and break each separately into a clean saucer.
Examine each for freshness and remove any pieces of shell before mixing with other eggs.

Mix thoroughly the yolks and whites and do not whip in air.
To prevent graininess of the yolks, add 1½ tablespoons sugar, 1½ tablespoons corn syrup OR ½ teaspoon salt per cup whole eggs, depending on intended use.
Strain through a sieve or colander to improve uniformity.
Package, allowing ½-inch headspace. Seal and freeze.

Separate eggs. Stir yolks gently.
To prevent graininess, add 1-½ tablespoons sugar, 1-½ tablespoons corn syrup OR ½ teaspoon salt per cup of egg yolks, depending on intended use.
Strain through a sieve.
Package, allowing ½-inch headspace. Seal and freeze. One tablespoon of the yolk mixture equals one egg yolk.

Gently mix whites; do not whip.
Strain through a sieve. No sugar or salt is needed.
Package, leaving ½-inch headspace. Seal and freeze. Two tablespoons of the egg-white mixture equal one egg white.

[edit] Tips

Another method of freezing a whole-egg mixture is to use ice trays. Measure 3 tablespoons of egg mixture into each compartment of an ice tray. Freeze until solid. Remove frozen cubes, and package in moisture-vapor resistant containers. Seal and freeze. Three tablespoons of the egg mixture (one cube) equal one whole egg.
If the compartments in your ice tray are too small to hold 3 tablespoons, use a muffin tin instead.
For times when you want to make half of a recipe that calls for one egg, put just half an egg (1½ tablespoons) in each ice tray compartment.

Freeze fresh eggs only. If in doubt, see How to Tell if Your Eggs are Rotten.
Wash hands and all utensils thoroughly after contact with raw eggs. Don't forget to wash the ice trays before reusing them to make ice.