(Updated by Pokemaster for Gen 7, and some of Gen 8)
Quick stat: the most common species categories are Dragon (8 Pokemon), Mouse (6), Mushroom (6), and Poison Pin (6).
Pokemon from different evolution lines:
Seed Pokemon:
Bulbasaur/Ivysaur/Venusaur
Sunkern
Flame Pokemon:
Charmeleon/Charizard
Flareon
Moltres
Infernape
Shellfish Pokemon:
Blastoise
Kabuto/Kabutops
Worm Pokemon:
Caterpie
Wurmple
Cocoon Pokemon:
Metapod/Kakuna
Silcoon/Cascoon
Butterfly Pokemon:
Butterfree
Beautifly
Tiny Bird Pokemon:
Pidgey
Spearow
Natu
Mouse Pokemon:
Rattata/Raticate
Pikachu/Raichu
Sandshrew/Sandslash
Poison Pin Pokemon:
Nidoran♀/Nidorina
Nidoran♂/Nidorino
Poipole/Naganadel
Drill Pokemon:
Nidoqueen
Nidoking
Rhydon/Rhyperior
Fairy Pokemon:
Clefairy/Clefable
Snubbull/Granbull
Fox Pokemon:
Vulpix/Ninetales
Fennekin/Braixen/Delphox
Balloon Pokemon:
Igglybuff/Jigglypuff/Wigglytuff
Qwilfish
Drifloon
Bat Pokemon:
Zubat/Golbat/Crobat
Woobat
Flower Pokemon:
Vileplume/Bellossom
Bellsprout
Mushroom Pokemon:
Paras/Parasect
Shroomish/Breloom
Foongus/Amoonguss
Poison Moth Pokemon:
Venomoth
Dustox
Mole Pokemon:
Diglett/Dugtrio
Drilbur
Puppy Pokemon:
Growlithe
Lillipup
Rockruff
Yamper
Tadpole Pokemon:
Poliwag/Poliwhirl/Poliwrath
Tympole
Sea Lion Pokemon:
Seel/Dewgong
Popplio
Bivalve Pokemon:
Shellder/Cloyster
Clamperl
Pincer Pokemon:
Kingler
Scizor
Egg Pokemon:
Exeggcute
Chansey
Dragon Pokemon:
Horsea/Seadra/Kingdra
Dratini/Dragonair/Dragonite
Salamence
Goodra
Star Shape Pokemon:
Staryu
Cleffa
Electric Pokemon:
Elekid/Electabuzz
Zapdos
Stag Beetle Pokemon:
Pinsir
Vikavolt
Fish Pokemon:
Magikarp
Feebas
Lightning Pokemon:
Jolteon
Electrike
Volcano Pokemon:
Quilava/Typhlosion
Entei
Scout Pokemon:
Sentret
Patrat
Light Pokemon:
Lanturn
Ampharos
Happiness Pokemon:
Togetic
Blissey
Mystic Pokemon:
Xatu
Flygon
Sun Pokemon:
Sunflora
Espeon
Volcarona
Darkness Pokemon:
Murkrow
Sableye
Royal Pokemon:
Slowking
Pyroar
Bagworm Pokemon:
Pineco/Forretress
Burmy/Wormadam
Armor Pokemon:
Donphan
Tyranitar
Bite Pokemon:
Poochyena/Mightyena
Drednaw
Water Bird Pokemon:
Pelipper
Ducklett
Emotion Pokemon:
Kirlia
Mesprit
Ninja Pokemon:
Ninjask
Greninja
Cheering Pokemon:
Plusle
Minun
Firefly Pokemon:
Volbeat
Illumise
Brutal Pokemon:
Sharpedo
Hydreigon
Coal Pokemon:
Torkoal
Rolycoly
Manipulate Pokemon:
Grumpig
Gothorita
Vibration Pokemon:
Vibrava
Palpitoad/Seismitoad
Cactus Pokemon:
Cacnea
Maractus
Meteorite Pokemon:
Lunatone
Solrock
Fruit Pokemon:
Tropius
Bounsweet/Steenee/Tsareena
Iceberg Pokemon:
Regice
Avalugg
Eon Pokemon:
Latias
Latios
Continent Pokemon:
Groudon
Torterra
Chimp Pokemon:
Chimchar
Grookey
Playful Pokemon:
Monferno
Pancham
Rabbit Pokemon:
Buneary/Lopunny
Scorbunny
Cave Pokemon:
Gabite
Druddigon
Thunderbolt Pokemon:
Electivire
Zebstrika
Fresh Snow Pokemon:
Glaceon
Vanillite
Ember Pokemon:
Pansear
Fletchinder
Drowsing Pokemon:
Musharna
Komala
Flowering Pokemon:
Lilligant
Gossifleur
Hostile Pokemon:
Basculin
Zweilous
Jewel Pokemon:
Carbink
Diancie
Pokemon from the same evolution line:
Bird Pokemon: Pidgeotto/Pidgeot
Weed Pokemon: Oddish/Gloom
Duck Pokemon: Psyduck/Golduck
Pig Monkey Pokemon: Mankey/Primeape
Psi Pokemon: Abra/Kadabra/Alakazam
Superpower Pokemon: Machop/Machoke/Machamp
Flycatcher Pokemon: Weepinbell/Victreebel
Jellyfish Pokemon: Tentacool/Tentacruel
Rock Pokemon: Geodude/Graveler
Fire Horse Pokemon: Ponyta/Rapidash
Magnet Pokemon: Magnemite/Magneton
Sludge Pokemon: Grimer/Muk
Gas Pokemon: Gastly/Haunter
Hypnosis Pokemon: Drowzee/Hypno
Ball Pokemon: Voltorb/Electrode
Licking Pokemon: Lickitung/Lickilicky
Poison Gas Pokemon: Koffing/Weezing
Vine Pokemon: Tangela/Tangrowth
Goldfish Pokemon: Goldeen/Seaking
Virtual Pokemon: Porygon/Porygon2/Porygon-Z
Spiral Pokemon: Omanyte/Omastar
Leaf Pokemon: Chikorita/Bayleef
Big Jaw Pokemon: Totodile/Croconaw/Feraligatr
Owl Pokemon: Hoothoot/Noctowl
Five Star Pokemon: Ledyba/Ledian
Wool Pokemon: Mareep/Flaaffy
Cottonweed Pokemon: Hoppip/Skiploom/Jumpluff
Long Tail Pokemon: Aipom/Ambipom
Water Fish Pokemon: Wooper/Quagsire
Sharp Claw Pokemon: Sneasel/Weavile
Lava Pokemon: Slugma/Magcargo
Jet Pokemon: Remoraid/Octillery
Kite Pokemon: Mantine/Mantyke
Dark Pokemon: Houndour/Houndoom
Wood Gecko Pokemon: Treecko/Grovyle
Mud Fish Pokemon: Mudkip/Marshtomp/Swampert
Compass Pokemon: Nosepass/Probopass
Iron Armor Pokemon: Aron/Lairon/Aggron
Meditate Pokemon: Meditite/Medicham
Whiskers Pokemon: Barboach/Whiscash
Clay Doll Pokemon: Baltoy/Claydol
Penguin Pokemon: Piplup/Prinplup
Starling Pokemon: Starly/Staravia
Cricket Pokemon: Kricketot/Kricketune
Head Butt Pokemon: Cranidos/Rampardos
Shield Pokemon: Shieldon/Bastiodon
Sea Weasel Pokemon: Buizel/Floatzel
Sea Slug Pokemon: Shellos/Gastrodon
Skunk Pokemon: Stunky/Skuntank
Toxic Mouth Pokemon: Croagunk/Toxicroak
Frost Tree Pokemon: Snover/Abomasnow
Grass Snake Pokemon: Snivy/Servine
Fire Pig Pokemon: Tepig/Pignite
Muscular Pokemon: Timburr/Gurdurr/Conkeldurr
Desert Croc Pokemon: Sandile/Krokorok
Proturtle Pokemon: Tirtouga/Carracosta
First Bird Pokemon: Archen/Archeops
Season Pokemon: Deerling /Sawsbuck
Floating Pokemon: Frillish/Jellicent
Gear Pokemon: Klink/Klang/Klinklang
EleFish Pokemon: Tynamo/Eelektrik/Eelektross
Cerebral Pokemon: Elgyem/Beheeyem
Axe Jaw Pokemon: Fraxure/Haxorus
Martial Arts Pokemon: Mienfoo/Mienshao
Automaton Pokemon: Golett/Golurk
Spiny Armor Pokemon: Quilladin/Chesnaught
Bubble Frog Pokemon: Froakie/Frogadier
Digging Pokemon: Bunnelby/Diggersby
Scatterdust Pokemon: Scatterbug/Spewpa
Single Bloom Pokemon: Flabébé/Floette
Mount Pokemon: Skiddo/Gogoat
Sword Pokemon: Honedge/Doublade
Mock Kelp Pokemon: Skrelp/Dragalge
Generator Pokemon: Helioptile/Heliolisk
Tundra Pokemon: Amaura/Aurorus
Soft Tissue Pokemon: Goomy/Sliggoo
Pumpkin Pokemon: Pumpkaboo/Gourgeist
Sound Wave Pokemon: Noibat/Noivern
Fire Cat Pokemon: Litten/Torracat
Bee Fly Pokemon: Cutiefly/Ribombee
Brutal Star Pokemon: Mareanie/Toxapex
Water Bubble Pokemon: Dewpider/Araquanid
Illuminating Pokemon: Morelull/Shiinotic
Toxic Lizard Pokemon: Salandit/Salazzle
Synthetic Pokemon: Type: Null/Silvally
Scaly Pokemon: Jangmo-o/Hakamo-o/Kommo-o
Land Spirit Pokemon: Tapu Koko/Tapu Lele/Tapu Bulu/Tapu Fini
Hex Nut Pokemon: Meltan/Melmetal
Now I'm done
(If there is anything I missed, please tell me.)