(A great piece of information by Klew Nu Farms)
Fill a container up with warm water. I use warm water. The reason for this is. Eggs are porous. If you put an egg in cold water, it will contract and draw any bacteria that is on the outside of the shell in through the pores. This is not good. So, if you use warm water, the egg will expand, and you will notice that little air bubbles form on the shell.
Put your eggs into the warm water, and look at them. A very fresh egg will sink to the bottom and lay on its side. Week old eggs will rest on the bottom but the fat end of the egg will rise up slightly. Three week old eggs will be balanced on pointy end with the fat end sticking up. Old eggs will be floating, bobbing along the surface of the water. These floaters should be tossed as they aren't any good to eat.
(Courtesy of forwarded mail from Jason Gan)