Once food is thawed in the refrigerator, you can safely refreeze most foods if they still have ice crystals, or if they are still cold "about 40 degrees F" and if you held them no longer than one or two days at 40 degrees F. There may be a loss of quality due to the moisture lost through defrosting.

After cooking raw foods which were previously frozen, it is safe to freeze the cooked foods. If previously cooked foods are thawed in the refrigerator, you may refreeze the unused portion. If you purchase previously frozen meat, poultry or fish at a retail store, you can refreeze if it has been handled properly.

Additional Resources:

http://lancaster.unl.edu/food/ciq-refreeze.shtml
http://lancaster.unl.edu/food/ftsep03.htm
http://www.uga.edu/nchfp/how/freeze.html