How long is it safe to keep eggs refrigerated?

Eggs can be part of a healthy diet. However, they are perishable, just like raw 
meat, poultry and fish. To be safe, they must be properly refrigerated and 
cooked. Also today some unborken shell eggs may contain bacteria that can make 
you sick unless the eggs are carefully handled. This bacteria is Salmonella 
enteritidis. While the number of eggs affected is less that 1 in ten thousand, 
there have been scattered out-breaks in the last few years.

Q. How long is it safe to keep eggs refrigerated? 
Use raw shell eggs within 3 to 5 weeks. Hard-cooked eggs will keep 1 week. Use 
leftover yolks and whites within 4 days.

How long is it safe to keep eggs frozen? 
About 6 months. You can freeze whites separately. For whole eggs, beat yolks 
and whites together.If eggs freeze accidentally in their shells, keep them 
frozen until needed. Defrost in the refrigerator. Discard any with cracked 
shells.

Also a home refrigerator should be running at 40 degrees Fahrenheit. Store them 
in the grocery carton in the coolest part of the refrigerator, not in the door. 

Also there is a USDA website which contains the EGG safety rules.Which are 
useful to follow.
http://www.masterstech-home.com/The_Kitchen/Articles/USDAEggSafetyRules.html

This is fine, but who keeps track of when they bought their eggs?  

Here's the trick:  fill a bowl with water and place the eggs in the water.  
Fresh eggs will sink because the yolk contains mostly dense proteins 
and a small air bubble.  As the egg ages, the dense stuff dries up and the 
air bubble becomes larger...making the egg less dense than the water 
and making bad eggs float.  
More information at the American Egg Board website: 
http://www.aeb.org/facts/facts.html

An amusing poem about this phenomenon at:
http://www.backwoodshome.com/articles/matthews53.html

[Note that there are several sources online claiming that you should do 
this test with -salt water- -- that is incorrect.  If you add enough salt, you 
can make any egg -- good or bad -- float.]

Although the information about the refrigeration of eggs is perfectly correct, 
please be aware that if you are going to cook anything more complex than fried 
eggs it is necessary to bring the eggs up to room temperature first.

Just leave them on the work surface for a couple of hours.

Personally, as a former chef, I never refrigerate eggs, but use them within a 
week or so.