What Are The Pokemon Egg Groups And What Pokemon Are In Each Group?

Egg groups are the compatibility of pokemon with each other. For example:
Ma chop in a different egg group from Rye oh lou, so it doesn't match up.
If it were paired up with a pokemon of the same egg group in the Daycare Center, it would produce an egg. The pokemon inside the egg would be the female pokemon you put in the Daycare.
Note: If a pokemon's egg group is "No eggs", it doesn't mean it can't lay an egg (would it be called "laying" if it's with pokemon?).
Note: Legendary pokemon can't lay eggs.
:D
Note: I wrote this same answer somewhere else on this site.

All your information is on this site: www.serebii.net
 
If you want to lay an egg, you need a female and a male of the same group. Also your egg will hatch into the female pokemon. But if you breed with a female ivysaur and a male pokemon in ivysaur's egg group, you will get a bulbasaur. Your egg will hatch into the first stage of evolution of the female pokemon.

Certain Pokemon can breed with different species, For example Gastly and a Shuppet can breed at the Day-Care and the resulting egg will be of the female pokemon. Of course pokemon with no gender cannot breed, the egg types are as follows Plant, Bug, Flying, Humanshape, Mineral, Intermediate, Ground, Water 1, Water 2, Water 3, Monster, Fairy and Dragon. JUst to let you know the Pokemon Ditto can breed with any pokemon except the ones that don't have a gender