Counter-part Pokémon are Pokémon that share many traits with each other but are usually unrelated in terms of evolution. Many of these counterparts are legendaries or version exclusives.
Generation I
Caterpie and Weedle
Both are Bug types with a 3 stage evolution - they reach the second stage at level 7 and the final stage at level 10. Both carry the same base stat total through each stage of their evolutionary lines. The Caterpie line is more common in Blue while the Weedle line is more common in Red. This is only true for Metapod and Kakuna in the remakes. Although they are not version-exclusive, both require a Generation III game (FireRed for Caterpie, LeafGreen for Weedle) to be inserted into the DS in order to be encountered in Sinnoh.
In Gold, Silver and their remakes, one can only catch both during the Bug-Catching Contest, otherwise only one can be caught depending on version (Caterpie in Gold and HeartGold, Weedle in Silver and SoulSilver). In Black and White they are fully version-exclusive.
Ekans and Sandshrew
Both are in the Field egg group and evolve at level 22. Ekans is exclusive to Red and FireRed and SoulSilver while Sandshrew is exclusive to Blue and LeafGreen. Both require a Generation III game (FireRed for Ekans, LeafGreen for Sandshrew) to be inserted into the DS in order to be encountered in Sinnoh.
Nidoran♂ and Nidoran♀
While they are almost the same (both Poison types in the Monster egg group evolving at level 16 and can evolve again using a Moon Stone), they are classified as two separate Pokémon and their evolutions are counterparts being male or female only. Nidoran♂ is more common in Red and FireRed, and Nidoran♀ is more common in Blue and LeafGreen.
Clefairy and Jigglypuff
Both have a gender ratio of 1 male to 3 females, are Fairy types, can both learn Sing, and evolve with the Moon Stone. Both also received a pre-evolution in Generation II.
Vulpix and Growlithe
Both are Fire types that evolve using the Fire Stone. Growlithe is exclusive to Red, Gold, FireRed and HeartGold, while Vulpix is exclusive to Blue, Silver, LeafGreen and SoulSilver. Both require a Generation III game (FireRed for Growlithe, LeafGreen for Vulpix) to be inserted into the DS in order to be encountered in Sinnoh.
Oddish and Bellsprout
They are Grass-Poison types with a 3 stage evolution line (evolving at level 21, then with a Leaf Stone). Oddish is exclusive to Red and FireRed while Bellsprout is exclusive to Blue and LeafGreen.
Meowth and Mankey
They have a 2 stage evolution line and evolve at Level 28. Both are also in the Field egg group. Meowth is exclusive to Blue, Silver and SoulSilver and Mankey is exclusive to Red, Gold and HeartGold.
Grimer and Koffing
They are both Poison-types in the Amorphous egg group. Grimer is more common in Blue, Sapphire, LeafGreen and Alpha Sapphire while Koffing is more common in Red, Ruby, FireRed and Omega Ruby.
Shellder and Staryu
Both are pure Water types in the Water 3 egg group and evolve using the Water Stone. Both their evolutions are dual-typed. Shellder is exclusive to FireRed and Y while Staryu is exclusive to LeafGreen and X.
Hitmonlee and Hitmonchan
Until it was revealed that they had a common pre-evolved form and another alternative evolution, they were considered counterparts. In Generation I, one cannot obtain both without trading.
Lickitung and Tangela
They are next to each other in the Johto Pokedex and gained an evolution in Generation IV (by level-up while holding a specific move). Both can learn Power Whip.
Scyther and Pinsir
Both are Bug types with a base stat total of 500 (as of Generation II). Scyther is exclusive to Red, FireRed and Diamond while Pinsir is exclusive to Blue, LeafGreen and Pearl. In Generation II and their remakes, one can only encounter them through the Bug-Catching Contest.
Electabuzz and Magmar
Both in the Human-Like egg group. Both received pre-evolutions in Generation II and evolutions in Generation IV (by trade while holding a specific item). Electabuzz is exclusive to Red, FireRed and White 2 while Magmar is exclusive to Blue, LeafGreen and Black 2.
Omanyte and Kabuto
They are the first fossil Pokémon introduced. Both are Rock-Water types in the Water 3 egg group that evolve at level 40. In Generation I, FireRed and LeafGreen, one cannot obtain both without trading. Omanyte is exclusive to HeartGold and Alpha Sapphire while Kabuto is exclusive to SoulSilver and Omega Ruby. Both are exclusive to Pokémon X as well.
Both also have Swift Swim and a critical hit-blocking ability (Shell Armor for Omanyte, Battle Armor for Kabuto) as their abilities. Both carry the same base stat total through each stage of their evolutionary lines.
Generation II
Murkrow and Misdreavus
Both received evolutions in Generation IV (by use of a Dusk Stone). Murkrow is exclusive to FireRed, Diamond and Black while Misdreavus is exclusive to LeafGreen, Pearl and White.
Ledyba and Spinarak
Both are Bug types that evolve once by level-up. Both are version exclusive (with Ledyba in Silver and SoulSilver and Spinarak in Gold and HeartGold). Spinarak can only be encountered at night while Ledyba can only be encountered in the morning. In Sinnoh, only their evolved forms can be encountered.
Tauros and Miltank
Both are based on bovine creatures and can only be one gender. Both also have a base stat total of 490. They are one of the less commonly acknowledged counterparts but often appear next to each other in some regional Pokédexes.
Espeon and Umbreon
Both evolve from Eevee during different times of day (Espeon during the day, Umbreon during the night). Both require high friendship in order to evolve from Eevee. Espeon learns Morning Sun while Umbreon learns Moonlight, both healing moves with different effectiveness during different times of day (in Generation II only).
Gligar and Sneasel
Both gained evolutions in Generation IV, evolving by leveling up at night while holding a specific item. Both carry the same base stat total through each stage of their evolutionary lines. Both have been version-exclusive - but in different generations, with Delibird acting as the counterpart exclusive to the other version.
Pinsir and Heracross
Both are Bug types with a base stat total of 500, and both gained Mega Evolutions in Generation VI. In Hoenn, both are found in different areas of the Safari Zone that require different types of bike to access. Pinsir is exclusive to Pokémon X while Heracross is exclusive to Pokémon Y.
Teddiursa and Phanpy
Teddiursa is exclusive to SoulSilver while Phanpy is exclusive to HeartGold. They are also version exclusive in Gold and Silver but whichever game they are exclusive to depends on the localization of the game (e.g. Teddiursa is exclusive to Japanese and Korean localizations of Silver while Phanpy is exclusive to all other localizations of Silver).
Both are in the Field egg group and have Pickup as their ability. Their evolutions have different abilities.
Skarmory and Mantine
Both are types with a base stat total of 465 (until Generation VII). Mantine is exclusive to Gold, LeafGreen and HeartGold while Skarmory is exclusive to Silver, FireRed and SoulSilver. Skarmory is tailored towards Defense while Mantine is tailored towards Special Defense.
Slowbro and Slowking
Both evolve from Slowpoke. Slowbro evolves by leveling up and Slowking evolves by trading while holding an item.
Lugia and Ho-Oh
These legendary version mascots are counterparts and both are leaders of Legendary Trios (Lugia is the master of Articuno, Zapdos, Moltres and Ho-Oh is the master of Raikou, Entei and Suicune). However, neither are exclusive to the versions they are mascots of (although they can be encountered at a lower level in those versions).
Generation III
Poochyena and Houndour
Both are Dark types based on canine animals. Poochyena is exclusive to Diamond and White while Houndour is exclusive to Pearl and Black. Both are exclusive to Pokémon X as well.
Silcoon and Cascoon
Although evolved from Wurmple they are counterparts because one evolves into a Dustox (Bug/Poison) and the other into a Beautifly (Bug/Flying).
Lotad and Seedot
Both are Grass-types, version exclusives and evolve under the same conditions (to get to the second stage, they need to level up to level 14 and to their final stage, they need to have a type of stone used on them). Both require the Generation III game they're exclusive to, to be inserted into the DS in order to be encountered in Sinnoh.
Both carry the same base stat total through each stage of their evolutionary lines. Both have an ability that doubles their speed during a weather condition.
Sableye and Mawile
Sableye is exclusive to Sapphire, SoulSilver and Alpha Sapphire while Mawile is exclusive to Ruby, HeartGold and Omega Ruby. Both require the Generation III game they're exclusive to, to be inserted into the DS in order to be encountered in Sinnoh. Both have a base stat total of 380. Both are dual-typed (as of Generation VI) and both also received Mega Evolutions in Generation VI (although Mawile's was released before Sableye's).
Ninjask and Shedinja
They both evolve from Nincada and represent life & death. Shedinja represents death because it is genderless, it belongs to a different egg group than Nincada and Ninjask, and its HP stat never changes.
Plusle and Minun
Despite having no relation in terms of evolution, they look almost identical and their abilities only work when used together. Minun are more common in Ruby and Plusle are more common in Sapphire. In Omega Ruby, Plusle can only be encountered through hordes while this is the case for Minun in Alpha Sapphire. In Black and White they are fully version-exclusive.
Volbeat and Illumise
Both are Firefly Pokémon, have a base stat total of 400 and can only be one gender. Unlike with Tauros and Miltank, one can hatch Volbeat or Illumise from any egg that Illumise breeds with a compatible Pokémon.
Zangoose and Seviper
The first known rivalry between two different species of Pokémon. Hence, both are version exclusive in Generation III, and both require the Generation III game they're exclusive to, to be inserted into the DS in order to be encountered in Sinnoh. However, both have a base stat total of 458, and both belong to the Field egg group and the Wild Plains friend area in Pokémon Mystery Dungeon: Red Rescue Team and Blue Rescue Team.
Solrock and Lunatone
They are both genderless, both the same type, both version exclusive and represent the sun and moon, which are opposites. Both have a base stat total of 440. Both require the Generation III game they're exclusive to, to be inserted into the DS in order to be encountered in Sinnoh.
Lileep and Anorith
They are fossil Pokemon based on marine organisms. Thus, both are partly Rock type and belong to the Water 3 egg group. Both evolve at level 40, and both carry the same base stat total through each stage of their evolutionary lines. While not version-exclusive in those games, one cannot obtain both in Ruby and Sapphire without trading. Both are exclusive to Pokémon Y.
Duskull and Shuppet
Both are Ghost types that evolve at level 37. Both have a base stat total of 295, with their evolutions' stats totalling up to 455. Duskull gained a further evolution in Generation IV, while Shuppet's evolved form received a Mega Evolution in Generation VI. Duskull is more common in Ruby and Omega Ruby while Shuppet is more common in Sapphire and Alpha Sapphire.
Huntail and Gorebyss
Both evolve from Clamperl by trade with a specific item, and have a base stat total of 485. Huntail is exclusively a wild Pokémon in Black, Black 2 and X while Gorebyss is exclusively a wild Pokémon in White, White 2 and Y, however Clamperl can be found and evolved in both versions.
Bagon and Beldum
Both evolve into pseudo-legendary Pokemon introduced in the same generation.
Latias and Latios
Both gender-exclusive and version-exclusive. In Generations III and IV, one must roam in order to capture whichever is exclusive to their game. An event allows the other (that would otherwise be unavailable) to be encountered and caught.
Groudon and Kyogre
Version exclusive version mascots which represent the land and the sea. Another example of a red and blue Counter-part.
Generation IV
Gardevoir and Gallade
Although both evolve from Kirlia, they are both very gender oriented, Gardevoir being feminine and Gallade being masculine.
Cranidos and Shieldon
Both are Fossil Pokémon (thus Rock type) that are version exclusive. Both are in the Monster egg group and evolve at level 30.
Stunky and Glameow
Both version exclusive (Stunky in Diamond and Glameow in Pearl) and both are used by Team Galactic's Jupiter and Mars respectively. They are also both a two stage evolution and part of the Field egg group. Both Pokémon and their evolution are unavailable in Platinum.
Bonsly and Mime Jr.
Both are pre-evolutions of earlier generation Pokémon. Both evolve by level-up after learning Mimic (and they can also learn Copycat. Neither are strictly version-exclusive; while Mime Jr. is normally found in Diamond and Bonsly in Pearl, one can obtain Mime Jr. in Pearl or Bonsly in Diamond through the Trophy Garden event unlocked after obtaining the National Pokédex.
Glalie and Froslass
Although both evolve from Snorunt, they are very gender oriented, with Glalie being masculine and Froslass being feminine.
Glaceon and Leafeon
Both are Eeveelutions that evolve when leveled up near a special rock.
Dialga and Palkia
Version mascots for Diamond and Pearl control Time and Space which are often used together.
Cresselia and Darkrai
Both are related to the moon, Darkrai causes bad dreams and Cresselia cures them.
Phione and Manaphy
They both represent the sea and they are parent and child that cannot evolve.
Generation V
Throh and Sawk
Both are Fighting-type and look similar as if wearing a judo uniform with a black belt. Both have a base stat total of 465. While not version-exclusive in Generation V, in Black and Black 2 Throh can only be encountered in rustling grass. This is true for Sawk in White and White 2. Both became version-exclusive in Generation VI.
Cottonee and Petilil
Both are version exclusive Grass-types that evolve with the Sun Stone. Both carry the same base stat total through each stage of their evolutionary lines.
Gothita and Solosis
Both are Psychic-types in a 3 stage evolution; the second stage is reached at level 32, and the final stage at level 41. Version exclusives.
Tirtouga and Archen
These fossil Pokemon are based on early turtles and birds. They became version-exclusive starting from Omega Ruby and Alpha Sapphire.
Karrablast and Shelmet
These Pokémon can only evolve when traded with each other.
Braviary and Mandibuzz
A male and female counterpart pair who are based on American settlers and native Americans. Both types that evolve at level 54. Version exclusives.
Heatmor and Durant
These are rivals like Seviper and Zangoose but are NOT version exclusive. However, they both have a base stat total of 484, a base experience yield of 169 and a catch rate of 90.
Reshiram and Zekrom
The ultimate counterparts represent Yin and Yang. Version exclusives.
Generation VI
Spritzee and Swirlix
A Fairy duo based on perfume and sweets. Version Exclusives. Both evolve by trade whilst holding a specific item.
Skrelp and Clauncher
These are sea creatures. Version Exclusives.
Tyrunt and Amaura
These fossil Pokemon represent aggression and passion. Both evolve at level 39 but at different times of day. They are also based on different groups of dinosaur (Tyrunt from theropods, Amaura from sauropods).
Xerneas and Yveltal
These counterparts represent X and Y. Version Exclusives.
Generation VII
Oranguru and Passimian
These are primates. Version Exclusives.
Turtonator and Drampa
These are Dragon Pokemon. Version Exclusives.
Solgaleo and Lunala
These counterparts represent day and night. Version Exclusives.