Often this subject appears in talks a lot, so we decided to explain how this is handled in the world of PMDe, so that various player characters’ backstories can be better put together.
When Pokemon procreate with another, there's a chance that an offspring happens in the form of an egg.
Since there is a wide range of different Pokemon species, cross breeding is bound to happen. As such, over the centuries, almost all forms of breeding and compatibility has been verified and documented in various genealogy books in PMD-e’s world.
What is known and documented is considered a "hard compatibility," in which procreation is certain between a male and a female. All listed examples are seen in the website veekun.com, like for example: Seviper & Serperior will produce an offspring. Also taken into account is that Nidorina and Nidoqueen follow the same hard compatibility as Nidoran female for this world (Nidoqueen and Nidorina cannot breed in the games).
Another thing to consider in the world of PMDe is that the species of the offspring isn't determined by the female. As an example, a male Lucario and a female Zangoose may have Riolu or Zangoose as children. Or if a clutch of eggs was made, perhaps both.
Some Pokemon species may have absolute sexes. For example, Kangaskhan are always female, while Tauros are always male. They may decide to identify themselves as the opposite gender, if they wish.
Sometimes, female Pokemon may lay unfertilized eggs. They appear as a wholly white egg, with no distinct features. Fertilized eggs will have a color pattern on their shell.
Pokemon with mythical status, such as Lugia, are capable of procreation themselves, and do indeed have a sex.
Material Pokemon that have no sex, such as Magnemite and Voltorb, do not procreate regularly, as their origin is a mystery. However, the very special Ditto is able to procreate and produce offspring of not only Material Pokemon, but Organic Pokemon as well.
Finally, not only are there "hard compatibilities"--such as in the main games-- but there are "soft compatibilities" as well for this world. These are incredibly rare, and as such are undocumented, however procreation is possible with scant odds. They seem to happen with Pokemon that are similar in features... for an example, Hydreigon & Flygon were never documented, so their chances are procreation are nil. But because they both are dragon-monsters, the chance does exist. Keep in mind that some Pokemon absolutely cannot breed with another, like a Finneon with a Teddiursa. They share no common traits! Obviously, we can’t oversee every “soft compatible” breeding example, so try to be reasonable. It stands that most mammalian-like Pokemon should have this slim chance of breeding with each other, most lizard-like ones with each other, etc... So use your best judgment if you’re using this for backstory or storyline related purposes, please. (And keep in mind, even if your Pokemon starts a family, they can’t add in the baby to their team without an appropriate recruit opportunity.)