Try breeding two pokemon from the same group or with ditto and you will get a egg

Rule 1: Pokémon belonging to group x cannot produce eggs.

Rule 2: Pokémon in groups 1-13 are only compatible with other pokémon in their groups.

Rule 3: Any pokémon belonging to groups 1-14 can be breeded successfully with a ditto.

Rule 4: Pokémon belonging to group 14 can only be breeded successfully with a ditto.

Rule 5: You cannot breed a ditto with another ditto.

Bring on the groups:

Group x: No eggs-group pokémon
articuno
cleffa
elekid
entei
ho-oh
igglybuff
lugia
magby
mew
mewtwo
moltres
nidoqueen
nidorina
pichu
raikou
smoochum
suicune
togepi
tyrogue
unown
zapdos

Group 1: Plant-group pokémon
bayleef
bellossom
bellsprout
bulbasaur
chikorita
exeggcute
exeggutor
gloom
hoppip
ivysaur
jumpluff
meganium
oddish
paras
parasect
skiploom
sunflora
sunkren
tangela
venusaur
victreebel
vileplume
weepinbell

Group 2: Bug-group pokémon
ariados
beedrill
butterfree
caterpie
forretress
gligar
heracross
kakuna
ledian
ledyba
matapod
paras
parasect
pineco
pinsir
scizor
scyther
shuckle
spinarak
venomoth
venonat
weedle
yanma

Group 3: Flying-group pokémon
aerodactyl
crobat
dodrio
doduo
farfetch'd
fearow
golbat
hoothoot
murkrow
natu
noctowl
pidgeot
pidgeotto
pidgey
skarmory
spearow
togetic
xatu
zubat

Group 4: Humanshape-group pokémon
abra
alakazam
drowzee
electabuzz
hitmonchan
hitmonlee
hitmontop
hypno
jynx
kadabra
machamp
machoke
machop
magmar
mr. mime

Group 5: Mineral-group pokémon
geodude
golem
graveler
onix
steelix
sudowoodo

Group 6: Indeterminate-group pokémon
gastly
gengar
grimer
haunter
koffing
magcargo
misdreavus
muk
slugma
weezing
wobbuffet

Group 7: Ground-group pokémon
aipom
ampharos
arbok
arcanine
cyndaquil
delibird
dewgong
diglett
donphan
dugtrio
dunsparce
eevee
ekans
espeon
farfetch'd
flaaffy
flareon
furret
girafarig
golduck
granbull
growlithe
houndoom
houndour
jolteon
mankey
mareep
meowth
miltank
nidoking
nidoran female
nidoran male
nidorino
ninetales
persian
phanpy
pikachu
piloswine
ponyta
primeape
psyduck
quagsire
quilava
raichu
rapidash
raticate
rattata
rhydon
rhyhorn
sandshrew
sandslash
seel
sentret
smeargle
sneasel
snubbull
stantler
swinub
tauros
teddiursa
typhlosion
umbreon
ursaring
vaporeon
vulpix
wooper

Group 8: Water 1-group pokémon
azumarill
blastoise
corsola
croconaw
delibird
dewgong
dragonair
dragonite
dratini
feraligatr
golduck
horsea
kabuto
kabutops
kingdra
lapras
mantine
marill
octillery
omanyte
omastar
politoed
poliwag
poliwhirl
poliwrath
psyduck
quagsire
remoraid
seadra
seel
slowbro
slowking
slowpoke
squirtle
totodile
wartortle
wooper

Group 9: water 2-group pokémon
chinchou
goldeen
gyarados
lanturn
magikarp
octillery
qwilfish
remoraid
seaking

Group 10: Water 3-group pokémon
cloyster
corsola
kabuto
kabutops
kingler
krabby
omanyte
omastar
shellder
tentacool
tentacruel

Group 11: Monster-group pokémon
ampharos
bayleef
blastoise
bulbasaur
charizard
charmander
charmeleon
chikorita
crocanaw
cubone
feraligatr
flaaffy
ivysaur
kangaskhan
lapras
larvitar
lickitung
mareep
marowak
meganium
nidoking
nidoran male
nidoran female
nidorino
pupitar
rhydon
rhyhorn
slowbro
slowking
slowpoke
snorlax
squirtle
totodile
tyranitar
venusaur
wartortle

Group 12: Fairy-group pokémon
azumarill
blissey
chansey
clefable
clefairy
granbull
hoppip
jigglypuff
jumpluff
marill
pikachu
raichu
skiploom
snubbull
wigglytuff

Group 13: Dragon-group pokémon
arbok
charizard
charmander
charmeleon
dragonair
dragonite
dratini
ekans
gyrados
horsea
kingdra
magikarp
seadra

Group 14: Gender unknown-group pokémon
electrode
magnemite
magneton
porygon
porygon2
starmie
staryu
voltorb

Group 15: Ditto group
ditto