Breeding

Breeding
One of the main reason genders were introduced when Gold/Silver came out was to allow two Pokemon to breed. Breeding is important for several reasons, the most important of which is:

Obtain Baby Pokemon - You can't find Pokemon like Pichu and Cleffa in the wild. In order to fill up your Pokedex, breeding is the only way to get them.
Get more of a rare Pokemon - Eevee, Aerodactyl, and many other species only appear once in a game, so breeding allows you to get multiple "copies" of the same species.
Have Pokemon learn bred-on moves - Some moves can't be learned in any other way besides through breeding. With breeding, you can get a Growlithe with Crunch, a Bagon with Hydro Pump, and many other cool moves that Pokemon can't naturally learn.

Breeding Basics
In order to breed, you need to go to the Daycare Center. In Ruby/Sapphire/Emerald, this is the house on Route 117. In Fire Red/Leaf Green, this is the house on Four Island.

Ruby/Sapphire/Emerald

Fire Red/Leaf Green

In order to breed, you need to give the old lady in the Daycare a male and female Pokemon from the same egg group.
The list of egg groups and the Pokemon in them are shown below (scroll you mouse over the image to see their names).
Remember that if an unevolved Pokemon is in an egg group, all their evolutions are in that egg group too (with the exception of baby Pokemon, Shedinja, Nidorina, and Nidoqueen).

Ground
Water 1
Water 2
Water 3
Monster
Plant
Flying
Bug
Fairy
Humanshape
Dragon
Indeterminate
Mineral
Genderless
No Eggs
Ditto

NOTE: Ditto can breed with any Pokémon except for those in the No Eggs group.
Genderless Pokémon cannot breed with anyone except Ditto.

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When will your egg be ready?
The chance of your two Pokémon producing an egg depends on their species and ID number. You can tell when your egg is ready when the old man stands outside of the fence. Talk to him to receive your egg.

Parents are same species and have different ID numbers
The old man says: The two seem to get along very well.
Chance of getting an egg: 70%

Parents are same species and have same ID numbers OR are different species and have different ID numbers.
The old man says: The two seem to get along.
Chance of getting an egg: 50%

Parents are different species and have same ID numbers.
The old man says: The two don't seem to like each other.
Chance of getting an egg: 20%

Parents are in different egg groups.
The old man says: They prefer to play with other Pokémon than each other.
Chance of getting an egg: 0%

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Inheriting moves
When the baby hatches out of the egg, it will know the moves it normally has at Lvl. 5 along with moves that may be passed down from the parents.

If both parents know the same Level-Up move, the baby will know it if it can also learn that move.
Example: A newly-hatched Torchic will know Slash if both parents know Slash.

If the father knows a TM move that the baby can learn, the baby will know that move.
Example: A newly-hatched Torchic will know Fire Blast if the father knows Fire Blast.

If the father knows a move that the baby can learn as an Egg move, the baby will know that move.
Example: A newly-hatched Torchic can know Counter, Endure, Reversal, Swagger, Rock Slide, or Smellingsalt if the father also knows those moves.

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Hatching your egg
In order to hatch the egg, you must walk around with it in your party. Each Pokémon egg requires a certain numbers of steps to take before it hatches.
Check the status of your egg. If it is making sounds, that means it's close to hatching.

In Emerald, having a Pokémon with the Magma Armor or Flame Body trait (Numel, Slugma, Camerupt, and Magcargo) in the same team as your egg will cut the number of steps you need to take by half. Having more than one of these Pokémon in the same team will have no additional effect.

# of Steps	Pokémon
1280
2560
3840
5120	All Pokémon not shown go here
6400
7680
8960
10240