Breeding rate greatly varies, depending on a number of factors such as the trainers, a Pokemon's heritage, and even held items.
These take precedence and override the normal breeding rules, and are very specific exceptions. The current breeding exceptions are Ditto, Zangoose and Seviper, and different Basculin formes.
Nature and some abilities are also influential in breeding, but have less of an impact than the standard breeding rules and exceptions. Note that a 0% chance is fixed and modifiers do not apply to it, so a 0% chance is always 0%.
The usual rules of Pokemon breeding are easy to follow, and explained in detail in this section.
The Pokemon will be of the mother's evolutionary family, unless in the case of oddities (see below), and will be of the first stage of the evolutionary family, once again unless in the case of a quirk.
The Pokemon inside the egg is already fully-formed when the egg is discovered, and nothing that can be done by the trainer affects it. Its IVs, ability, gender, moveset and shininess are already decided when the egg is received.
Oddities are special Pokemon or items that do not follow the usual rules, or override those rules just as with the breeding exceptions.
Ditto is the most common oddity, as it can breed with any Pokemon that is not in the No eggs egg group, including several genderless Pokemon. The offspring will be of the non-Ditto parent's evolutionary family, once more unless there are other oddities or quirks at hand.
Nidoran ♀ and Illumise are known as counterpart Pokemon. If bred with any compatible Pokemon, including Ditto, the egg will hatch into the male or female counterparts depending on the egg's gender. For Nidoran ♀, the egg may hatch into Nidoran ♀ or Nidoran ♂, and for Illumise, it will hatch into Illumise if female, and Volbeat if male. Note that only the females of the species are able to produce eggs that hatch into both counterparts. Nidoran ♂ and Volbeat will always only produce more Nidoran ♂ and Volbeat eggs unless bred with their female counterparts.
Other Pokemon will only produce eggs that hatch into their baby Pokemon evolutionary stage if they hold a specific Incense while breeding, and will otherwise produce a basic Pokemon. Marill's family only produces Azurill with the Sea Incense, Wobbuffet only produces Wynaut with the Odd Incense, Roselia's family only produces Budew with the Rose Incense, Chimecho only produces Chingling with the Pure Incense, Sudowoodo only produces Bonsly with the Rock Incense, Mr. Mime only produces Mime Jr. with the Odd Incense, Chansey's family only produces Happiny with the Luck Incense, Mantine only produces Mantyke with the Wave Incense, and Snorlax only produces Munchlax with the Full Incense.