Egg Group
Pokémon first were able to breed in the Second Generation games Pokémon Gold and Silver. Breeding allowed pokémon to pass down stats and moves. Moves usually are inherited from the male pokémon while the child takes on the form of the mother in her basic form. A baby would hatch out of an egg after so many steps in the game and would always be at level five.
Breeding continues in the current Pokémon games as IVs and DVs are also passed down along with moves and stats. Usually you have a 50/50 chance of getting male or female Pokémon. If the pokémon is a Starter Pokémon,certain dragon types, Eevee, Snorlax, Chansey and others, you get a a different ratio. Here are the Egg Groups:
Ditto
Ditto can breed with any Pokémon except for Legendary Pokémon Ditto can also breed with Pokémon such as: Baltoy, Voltorb, Porygon and other genderless Pokémon.
Can't Breed
The following pokémon are incapable of breeding:
Shedinja, Azurill, Magnemite, Magneton, Voltorb, Electrode, Lunatone, Solrock, Baltoy, Claydol, Igglybuff, Staryu, Starmie, Pichu, Wynaut, Beldum, Metang, Metagross, Regirock, Regiice, Registeel, Latias, Latios, Kyogre, Groudon, Rayquaza, Jirachi, Deoxys, Nidorina, Nidoqueen, Articuno, Zapdos, Moltres, Mewtwo, Mew, Cleffa, Togepi, Unown, Tyrogue, Smoochum, Elekid, Magby, Raikou, Entei, Suicune, Lugia, Ho-Oh, Celebi.
Group 1: Plant
Many Grass-type pokémon belong in this group:
Lotad, Lombre, Ludicolo, Seedot, Nuzleaf, Shiftry, Shroomish, Breloom, Oddish, Gloom, Vileplume, Bellossom, Cacnea, Cacturne, Tropius, Bulbasaur, Ivysaur, Venusaur, Paras, Parasect, Bellsprout, Weepingbell, Victreebel, Exeggcute, Exeggcutor, Tangela, Chikorita, Bayleef, Meganium, Hoppip, Skiploom, Jumpluff, Sunkern, Sunflora.
Group 2: Bug
Many Bug-type pokémon belong in this group:
Wurmple, Silcoon, Beautifly, Cascoon, Dustox, Surskit, Masquerain, Nincada, Ninjask, Volbeat, Illumise, Trapinch, Vibrava, Flygon, Pinsir, Heracross, Caterpie, Metapod, Butterfree, Weedle, Kakuna, Beedrill, Paras, Parasect, Venonat, Venomoth, Scyther, Ledyba, Ledian, Spinarak, Ariados, Yamna, Pineco, Forretress, Gligar, Scizor, Shuckle.
Group 3: Flying
This is the group where most of the Flying-type pokémon are:
Taillow, Swellow, Wingull, Pellipper, Zubat, Golbat, Crobat, Doduo, Dodrio, Skarmory, Swablu, Altaria, Natu, Xatu, Pidgey, Pidgeotto, Pidgeot, Spearow, Fearow, Farfetch'd, Aerodactyl, Hoothoot, Noctowl, Togetic, Murkrow.
Group 4: Humanshape
The humanoid pokéemon belong here including many Fighting-type Pokémon and Psychic-type pokémon
Abra, Kadabra, Alakazam, Makuhita, Hariyama, Sableye, Machop, Machoke, Machamp, Meditite, Medicham, Volbeat, Illumise, Spinda, Cacnea, Cacturne, Drowzee, Hypno, Hitmonlee, Hitmonchan, Hitmontop, Chansey, Blissey, Mr. Mime, Jynx, Electabuzz, Magmar.
Group 5: Mineral
Rock-type Pokémon, Ground-type Pokémon and a Steel-type Pokémon belong in this group.
Geodude, Graveler, Golem, Nosepass, Onix, Steelix, Snorunt, Glalie, Porygon, Porygon 2, Sudowoodo.
Group 6: Indeterminate
Poison-type Pokémon, Ghost-type Pokémon and a few others beclong in this group.
Ralts, Kirila, Gardevoir, Gulpin, Swalot, Slugma, Magcargo, Grimer, Muk, Koffing, Weezing, Castform, Shuppet, Banette, Duskull, Dusclops, Chimecho, Wobbuffett, Gastly, Haunter, Gengar, Misdreavus.
Group 7: Ground
Fire-type, Water-type, Normal-type, Dark-type, Electric-type and Ice-type Pokémon belong to this group.
Torchic, Combusken, Blaziken, Poochyena, Mightyena, Zigzagoon, Linoone, Seedot, Nuzleaf, Shiftry, Slakoth, Vigoroth, Slaking, Whismur, Loudred, Exploud, Skitty, Delcatty, Mawile, Electrike, Manectric, Wailmer, Wailord, Numel, Camerupt, Torkoal, Spoink, Sandshrew, Sandslash, Spinda, Zangoose, Seviper, Kecleon, Absol, Vulpix, Ninetales, Pikachu, Raichu, Psyduck, Golduck, Girafarig, Phanpy, Donphan, Rhyhorn, Rhydon, Spheal, Sealeo, Walrein, Rattata, Raticate, Ekans, Arbok, Nidoran female, Nidoran male, Nidorino, Nidoking, Diglett, Dugtrio, Growlithe, Arcanine, Ponyta, Rapidash, Farfetch'd, Seel, Dewgong, Tauros, Eevee, Vaporeon, Jolteon, Flareon, Espeon, Umbreon, Cyndaquil, Quilava, Typhlosion, Sentret, Furret, Mareep, Flaaffy, Ampharos, Aipom, Wooper, Quagsire, Dunsparce, Snubbull, Granbull, Sneasel, Teddiursa, Ursaring, Swinub, Piloswine, Delibird, Houndour, Houndoom, Smeargle, Milktank.
Group 8: Water 1
Water Pokémon Part 1.
Mudkip, Marshtomp, Swampert, Lotad, Lombre, Ludicolo, Wingull, Pellipper, Surskit, Masquerain, Goldeen, Seaking, Marill, Azumarill, Corphish, Crawdaunt, Feebas, Milotic, Psyduck, Golduck, Spheal, Sealeo, Walrein, Clamperl, Huntail, Gorebyss, Corsola, Horsea, Seadra, Kingdra, Squirtle, Wartortle, Blastoise, Poliwag, Poliwhirl, Poliwrath, Politoed, Slowpoke, Slowbro, Seel, Dewgong, Lapras, Omanyte, Omastar, Kabuto, Kabutops, Dratini, Dragonair, Dragonite, Totodile, Croconaw, Feraligatr, Wooper, Quagsire, Remoraid, Octillery, Delibird, Mantine.
Group 9: Water 2
Water Pokémon Part 2.
Goldeen, Seaking, Magikarp, Gyarados, Carvanha, Sharpedo, Wailmer, Wailord, Barboach, Whishcash, Relicanth, Chinchou, Lantern, Luvdisc, Shellder, Cloyster, Quilfish, Remoraid, Octillery.
Group 10: Water 3
Water Pokémon Part 3.
Tentacool, Tentacruel, Corphish, Crawdaunt, Lileep, Cradily, Anorith, Armaldo, Corsola, Omanyte, Omastar, Kabuto, Kabutops, Remoraid, Octillery.
Group 11: Monster
These are Pokémon that fit the "monster" characteristic.
Treecko, Grovyle, Sceptile, Mudkip, Marshstomp, Swampert, Whismur, Loudred, Exploud, Aron, Lairon, Aggron, Bulbasaur, Ivysaur, Venusaur, Charmander, Charmeleon, Charizard, Squirtle, Wartortle, Blastoise, Nidoran Female, Nidoran Male, Nidorino, Nidoking, Slowpoke, Slowbro, Slowking, Cubone, Marowak, Likitung, Kangaskhan, Lapras, Snorlax, Chikorita, Bayleef, Meganium, Totodile, Croconaw, Feraligatr, Mareep, Flaaffy, Ampharos, Larvitar, Pupitar, Tyranitar.
Group 12: Fairy
These Pokémon are considered to be shaped like fairies, and as such are part of the Fairy breeding group. They are:
Shroomish, Breloom, Marill, Azumarill, Skitty, Delcatty, Mawile, Plusle, Minun, Roselia, Jigglypuff, Wigglytuff, Castform, Pikachu, Raichu, Snorunt, Glalie, Clefairy, Clefable, Hoppip, Skiploom, Jumpluff, Snubull, Granbull.
Group 13: Dragon
Dragon-type Pokémon, along with those that resemble Dragons, are in this group.
Treecko, Grovyle, Sceptile, Magikarp, Gyarados, Swablu, Altaria, Seviper, Feebas, Milotic, Horsea, Seadra, Kingdra, Bagon, Shelgon, Salamence, Charmander, Charmeleon, Charizard, Ekans, Arbok, Dratini, Dragonair, Dragonite.
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 accessable to certain Pokémon to be legal, like Heal Bell on Blissey..