Pokemon Eggs can be sometimes be found if you leave a male and female Pokemon at the Day-Care. Leaving Pokemon like Volbeat and Illumise at the Day-Care will have an egg, but chances are it is another Volbeat or Illumise. Breeding Pokemon that are types weaker or stronger than eachother (e.g., Treecko and Squirtle) will not have an egg (However, there are a few exceptions). Also, leaving Pokemon like Nidoran♀ and Nidoran♂ will have an egg, but just like Volbeat and Illumise, the contents of the egg will be another Nidoran. (Either male or female). Ditto can breed into any egg. When you breed a Manaphy with a Ditto, you will get a Phione. The only way to get a genderless Pokemon in a egg is to breed with a Ditto (Except in Generation III).
The pokemon you leave will have an egg under the following known conditionsEdit
-Ditto and any other Non-legendary (Gen.3/4)