From Bulbapedia, the community-driven Pokémon encyclopedia.
Egg groups are categories which determine which Pokémon are able to interbreed in Pokémon breeding. A Pokémon may belong to either one or two egg groups.
Egg groups are decided by biological traits, which overall serves to allow Pokémon which are biologically similar to breed. However, there are some oddities which have been noted within egg groups: for example, the Ground egg group's standards are particularly broad, and many illogical pairings can be noted within it.
Many Pokémon are included in two different egg groups and can form what are known as breeding chains. These link many unrelated Pokémon together, allowing moves that would not normally be accessible to certain Pokémon to be legal, like Heal Bell on Blissey.
TMs are also passed down through breeding through male Pokémon. Doing this would cause the moves to appear in the Pokémon's moveset if said Pokémon can learn the move via TM or Egg Move.
Due to its ability to transform its shape, Ditto can breed with any Pokémon except for those in the no eggs group. The following genderless Pokémon can only breed with Ditto:
This group is Group X. The Pokémon within it are incapable of breeding. Mostly, this category consists of legendary Pokémon and baby Pokémon; however, for unknown reasons, Nidorina and Nidoqueen are a part of this group as well.
This group is Group 1. Many Grass-type Pokémon belong to this group.
This group is Group 2. Many Bug-type Pokémon belong to this group.
This group is Group 3. This is the group to which most of the Flying-type Pokémon belong.
This group is Group 4. The humanoid Pokémon belong here, including many Fighting-type and Psychic-type Pokémon.
This group is Group 5. These Pokémon seem to be made of minerals, rather than organic matter. Thus, in this group can be found a small mix of Rock-type Pokémon, Ground-type Pokémon, Ice-type Pokémon and Steel-type Pokémon.
This group is Group 6. Poison-type Pokémon, Ghost-type Pokémon and a few others belong in this group.
This group is Group 7. It encompasses many land-dwelling Pokémon (as well as a few sea-dwelling ones), and contains many types of Pokémon, including Fire-type, Water-type, Normal-type, Dark-type, Electric-type and Ice-type Pokémon.
The presence of both Skitty and Wailord in this group has led to HSOWA gaining popularity in some sections of the fandom.
This group is Group 8. This is the group to which most of the Water-type Pokémon belong.
This group is Group 9. This is the group to which some Water-type Pokémon belong.
This group is Group 10. This is the group to which some Water-type (and some non-water-type) Pokémon belong.
This group is Group 11. It contains Pokémon that are monster-like.
This group is Group 12. The Pokémon in this group are considered to be fairy-like in form.
This group is Group 13. Dragon-type Pokémon, along with those that resemble dragons or serpents, are in this group.