If they have something nasty on them that you want to wash off, it's best to do it with very warm water. Water colder than the egg can cause the egg to absorb the bacteria on the outside.
If there's not something on it, it is best not to wash it. When the hen lays the egg, she gives it a protective "bloom," a film that protects the inside of the egg from contamination. I do not wash any of my eggs, even if they're dirty, until i'm ready to crack them. Then i wash under very warm water, like i said, just so that i don't accidentally crack the grossness into my actual edible egg.
Here is a great article about a study done on the storage of fresh eggs.
http://www.motherearthnews.com/Sustainable-Farming/1977-11-01/Fresh-Eggs.aspx
In short, the egg-sperimenters found that the best way to store eggs is unwashed in the refrigerator. And they will last months! I believe it was 6-8 months. I would never toss a 2 week-old egg. The eggs you buy in the store are usually at least a month old before you buy them.
Your egg is definitely safe to eat, unless you have recently medicated your hens with something that humans should not ingest.
Also, fresh eggs are good for a week or more, stored right on your counter at room temperature. And i believe that many cooks/chefs will recommend using room temperature eggs for better baking. Eggs are not nearly as fragile as some of us have been led to believe. Just think about Caroline Ingalls carrying her basket of eggs to town in a basket in the heat. Not once refrigerated....guaranteed.