Eggs can last longer in when you keep them in the refrigerator, but how do you know how long they can be considered "fresh?" Just drop the eggs into a bowl of tap water. If you egg is fresh, it will sink and if it is past its prime, it will float. This is because the air pocket inside - which you have probably noticed when you are shelling hard-boiled eggs - gets larger as the egg ages, causing it to float.
If you want to keep your eggs longer than a few weeks, you can freeze them. Eggs can be removed from their shells and frozen for up to a year. When you want to use them, just let them defrost in the refrigerator. Either gently stir the yolk and white together before freezing, or separate the two components and freeze separately. Egg whites freeze and thaw particularly well, but the yolks can develop lumps as they defrost. To avoid this, simply stir a bit of salt (for eggs intended for savory dishes) or sugar/corn syrup (for sweet destined eggs) into your egg yolk before freezing. I also recommend labeling the eggs, lest you end up with overly salty pancakes some morning.
Of course, you could just use up your eggs quickly, as Mr. Breakfast reminds us with this verse:
Use your eggs the week you buy them
Poach them, boil them, cook or fry them
Throw them out when they expire
And to the store more eggs acquire
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