everyone has their own opinion on this. But there are several ways to wash eggs if that is your choice:
PUBLICATION 8120
Hatching Egg Sanitation: The Key Step in Successful Storage and Production
RALPH A. ERNST, University of California Cooperative Extension Poultry Specialist, University of California, Davis
PRODUCING CLEAN EGGS
Sanitation is essential in successful hatching egg production, and the most important step in egg sanitation is producing nest-clean eggs. This requires a carefully planned management system. The following practices have proven to be useful in producing clean eggs for hatching and in keeping the eggs clean until they are set in incubators.
Maintain birds on wire, plastic, or wooden slatted floors whenever possible. However, some commercial strains of chickens and turkeys do not produce well in this environment and must have litter floors in part or all of the house.
To keep floor eggs (eggs laid on the floor) to a minimum, provide 1 nest for every 4 hens. Be sure nests are in place before egg production starts.
Keep nests filled with clean nesting material such as wood shavings, rice hulls, or nest pads.
Collect eggs frequently (at least 4 times a day).
Exclude hens from nests at night. This prevents hens from becoming broody (attempting to incubate eggs and remain on the nest) and keeps nests cleaner.
Maintain dry litter at all times.
Collect eggs on clean, sanitized plastic flats or in clean egg baskets.
Separate cracked, stained, heavy, or dirty eggs as you collect them, and dont incubate them.
Sanitize clean eggs as soon as possible after collection. Sanitation kills microbes on the outside of the shell. It does not kill all of the microbes that have penetrated the shell.
Always wash hands thoroughly with a disinfectant soap before handling eggs.
Cool eggs overnight in flats before placing them in cases. If eggs are to be stored, place them in a clean room held at 55º to 68ºF (12.8º to 20.0ºC) and 75 percent relative humidity (see table 1).
Prevent eggs from sweating (forming surface moisture from condensation) when they are moved from cold storage into a warmer room. You can prevent sweating by putting eggs in trays in a temperature-controlled room (see table 2).
UNIVRSITY OF CALIFORNIA
Division of Agriculture and Natural Resources
http://anrcatalog.ucdavis.edu
I have this as a PDF. There are several others that refer to washing eggs.
Many people believe when you wash them you remove the "bloom" the hen applies to protect the egg from Bacteria. So you will get many differing opinions on this issue.
ETA: my spelling errors are fixed.