Dud Eggs are a new feature introduced on the 15th March 2013. When breeding dragons there is a very low chance to produce an infertile "dud" egg, and any breedable dragon can produce these dud eggs, including donation dragons. This is the only way to collect egg sprites on the site so far. They are collected under http://taleofdragons.net/eggs and the eggs were originally arranged by release date but are now ordered by the order in which you collect them. Dud eggs were confirmed by Corteo to not affect or replace breeding success.
It is not possible to obtain duplicate eggs of the same breed.