Some RBY counters:
Dewgong:
http://www.smogon.com/rb/pokemon/dewgong
"Lapras and Starmie resist both of its STABs and can make short work of it with Thunderbolt. Zapdos and Jolteon pose a threat to Dewgong with their powerful electric attacks, while Chansey takes little damage from any of its moves. Venusuar and co can put Dewgong to sleep or decimate it with STAB Grass attacks as long as they watch out for Blizzard"
Machamp:
http://www.smogon.com/rb/pokemon/machamp
"Alakazam, Starmie, Dragonite, and Zapdos can all switch in on Machamp, but an unlucky Body Slam paralysis can spell doom for all four of them. More foolproof counters include Exeggutor and Slowbro, who both take little damage from all of Machamp's attacks and can hit back hard. Articuno and Moltres are less-used but very viable counters for Machamp as long as they watch out for Rock Slide."
Blastoise:
http://www.smogon.com/rb/pokemon/blastoise
"Zapdos and Jolteon have ample oppurtunity to switch in on Blastoise; with his mediocre Special, Blizzard is only a 3HKO on Zapdos. Lapras and Starmie resist both Surf and Ice Beam, although Starmie doesn't like getting hit with Body Slam. Venusuar is very rarely 2HKOd by Blizzard, but outspeeds Blastoise and carries a reliable sleep move as well as Razor Leaf.
In UU, Electabuzz and Magneton give Blastoise loads of trouble with a STAB Thunderbolt. Golduck and Poliwrath can set up on Blastoise with Amnesia and take little damage from it's attacks."
Butterfree:
http://www.smogon.com/rb/pokemon/butterfree
"Chansey loves switching in on a Stun Spore, and Exeggutor takes little from both of Butterfree's attacks. Really, anything not weak to Grass or Psychic will suffice.
Specific UU counters include Tangela, who can threaten Stun Spore, and Fire types such as Arcanine, whose STAB Fire Blast sends Butterfree running"
Cloyster
http://www.smogon.com/rb/pokemon/cloyster
"Water types such as Starmie, Lapras, and Slowbro, resist both Clamp and Blizzard. Cloyster usually falls to special attackers that can hit it super effective, such as Jolteon, Venusuar, and Victrebell."
Dugtrio:
http://www.smogon.com/rb/pokemon/dugtrio
"Starmie, and Slowbro are both bulky enough to take Dugtrio's hits and return STAB Surfs. Aerodactyl resists it's attacks, outspeeds it, and has no problem tearing through Dugtio's tissue-like defenses. Exeggutor perpetually walls Dugtio, being only 4HKOd by Slash."
Fearow:
http://www.smogon.com/rb/pokemon/fearow
"Golem and Rhydon take nothing from it's attacks, as does Zapdos. Anything that can hit it with a super effective attack will make short work of Fearow.
If you're playing in UU, Onix stops Fearow cold, and Marowak takes little from its attacks. Electabuzz, while not as easy to switch in due to Double-Edge, carries STAB Thunderbolt to fry Fearow."
Flareon:
http://www.smogon.com/rb/pokemon/flareon
"Bulky waters such as Slowbro and Starmie can easily switch in on Flareon, and while Starmie doesn't like to be paralyzed, it loves to be burned. Golem and Rhydon also make good counters with their resistances. In UU, Omastar and Kabutops make short work of Flareon.
Onix resists all of Flareon's moves, although although a Burn from Fire Blast will halve his already pitiful attack. Aerodactyl is the only other Rock type in UU, so he gets a special mention."
Hitmonchan:
http://www.smogon.com/rb/pokemon/hitmonchan
"Hitmonchan can't do much to Gengar and his immunity to Normal and Fighting, but keep in mind that Seismic Toss can hit Ghost types in RBY. Exeggutor takes little damage from any of Hitmonchan's attacks, as does Slowbro. Zapdos, Alakazam, and Starmie are all stellar counters, but must beware of Body Slam.
In UU, Butterfree has a quadruple resist to Fighting and can return a hit with a super effective Psychic. Tangela can paralyze Hitmonchan, and Golduck can set up on it."
Lickitung:
http://www.smogon.com/rb/pokemon/lickitung
"Exeggutor and Machamp deal with Lickitung pretty easily. Golem and Rhydon, though weak to Earthquake, hardly fear Lickitung's pitiful 55 base Attack. Slowbro can easily set up on Lickitung.
Taking UU into account, fighting types such as Hitmonlee and Primape make short work of Lickitung. Aerodactyl resists its attacks, although it hates an unlucky paralysis."
Magneton:
http://www.smogon.com/rb/pokemon/magneton
"Golem and Rhydon take nothing at all from the Electric/Normal type combination Magneton uses, as does Onix if you're playing in UU. Chansey doesn't care about Thunderbolt and can Softboiled off Double-Edge damage while chipping away at Magneton with Ice Beam. Exeggutor resists Electric and has a high enough Defense to laugh at Double-Edge.
Honorable mention goes to Tangela, who resists Thunderbolt and shrugs off Double-Edge."
Mr. Mime:
http://www.smogon.com/rb/pokemon/mr_mime
"Exeggutor takes little from Mr. Mime's attacks, although it can't do much in return if Sleep Clause is already in effect. Chansey is more reliable in that she can fearlessly switch in and Thunder Wave Mr. Mime and Softboiled off any damage."
Kingler:
http://www.smogon.com/rb/pokemon/kingler
"Gengar takes little from Surf and nothing from Body Slam, making him the best Kingler counter you can have. Exeggutor easily takes the Water attacks, and his defense allows him to shrug off a boosted Body Slam in order to get a Sleep Powder in. Venusaur can do the same thing, although his defenses aren't quite as steller.
Kingler easily falls to special attacks, so Zapdos is a good switchin. Jolteon and Venusaur can all hit him for super effective damage with a STAB attack, and they outspeed him to boot.
In UU, Tangela resists Water and can paralyze with Stun Spore or set up with Growth and Mega Drain. Golduck can Amnesia in its face, although it doesn't like Swords Danced Body Slams. Electabuzz can threaten with STAB Thunderbolt if you can get it in; ditto with Magneton."
Nidoking:
http://www.smogon.com/rb/pokemon/nidoking
"Alakazam works well as a counter, as does Articuno. Blizzard is not enough to deter Exeggutor, who can force Nidoking to switch by threatening Psychic. Lapras and Starmie are able to fire off STAB Surfs at Nidoking, but have trouble switching in for fear of Thunder and Body Slam."
Nidoqueen:
http://www.smogon.com/rb/pokemon/nidoqueen
"Exeggutor is not deterred by Blizzard, and can shoot STAB Psychics in Nidoqueens direction if she doesn't switch. Alakazam and Starmie both are good counters, though Starmie fears a super effective Thunder. Articuno can switch in on almost everything, as even Thunder is not enough to strike fear into its massive Special."
Parasect:
http://www.smogon.com/rb/pokemon/parasect
"As long as Parasect isn't packing Stun Spore, Gengar has nothing to fear from the overgrown mushroom. Likewise, Moltres can use it to set up Agility for a Fire Spin sweep. Parasect is unbelievably frail when it comes to fire moves; Fire Blast from Arcanine, Charizard, or Ninetales can OHKO it. Lapras can deal huge amounts of damage with Blizzard, and Dodrio OHKOs with Drill Peck. Obviously, all counters on this list need to beware of Spore.
In UU, Aerodactyl causes serious problems as do the Fire types previously mentioned."
Pinsir:
http://www.smogon.com/rb/pokemon/pinsir
"Given the standard set, Pinsir has no way to damage Gengar, whose Thunderbolt makes short work of Pinsir. Exeggutor's good defense allows him the ability to switch in with impunity, and his high Special Attack gives him the ability to take down Pinsir with Psychic. Zapdos can switch in on anything, although Body Slam has an ugly chance of paralysis.
Tangela doesn't fear anything Pinsir has, if you're looking for a UU counter. Arcanine can switch in and threaten with a STAB Fire Blast, but doesn't like getting paralyzed."
Rapidash:
http://www.smogon.com/rb/pokemon/rapidash
"Starmie gets special mention for the ability to outspeed Rapidash before an Agility and nail it with Surf. Slowbro doesn't take much damage from any of Rapidash's attacks and can Amnesia up in it's face, while Alakazam can outspeed it and Recover when need be. Chansey can paralyze it, but an additional Agility will give it back it's speed.
Golduck and Poliwrath take little from Rapidash's attacks and can set up on it with Amnesia. Vaporeon's 130 base HP and 110 base Special laugh at Rapidash's special moves and Surf can seriously damage it."
Raticate:
http://www.smogon.com/rb/pokemon/raticate
"Gengar is a top-notch Raticate counter, but even he loses half his health on the switch - Super Fang affects Ghosts in RBY. Basically, whatever you switch in is going to have to sacrifice 50% to Super Fang, so the best option is just to hit it really hard with the pokemon you currently have in. Excellent are pokemon such as Starmie that get Recover; use it immediately after he Super Fangs or you'll be OHKOd by Hyper Beam.
Porygon has Thunder Wave and Recover, but must beware a Hyper Beam after a Super Fang; it will without a doubt kill him. Tangela isn't killed and packs Stun Spore as well as possible recovery in the for of Mega Drain + Growth."
Scyther:
http://www.smogon.com/rb/pokemon/scyther
"Gengar takes no damage from Scyther's astonishing array of Normal-typed moves. Likewise, Golem and Rhydon have a field day exploiting Scyther's lack of any move that can hit Rock types.
Onix is basically a UU Rhydon in that he takes nothing from Scyther's attacks. Aerodactyl outspeeds and can hit Scyther with Double-Edge or Fire Blast."
Seaking:
http://www.smogon.com/rb/pokemon/seaking
"Gengar takes no damage from Seaking's Normal moves, and hardly any more from Surf or Blizzard. Starmie and Lapras switch in easily and threaten with Thunderbolt. Zapdos hits Seaking for super effective damage and is only 3HKOd by Blizzard in return; Jolteon fares even better against Seaking's Surf. Grass types such as Venusaur are also good choices.
Seaking ends up fighting a losing battle against UU mainstays such as Tangela, who can recover off Seaking's damage with Mega Drain, and Golduck, who can Amnesia up while taking little damage. Electabuzz and Magneton both force Seaking to run in fear of STAB Thunderbolt."
Snorlax:
http://www.smogon.com/rb/pokemon/snorlax
"Gengar fares well against Snorlaxes without Earthquake, while Cloyster's high Defense let him handle non-Amnesia Snorlax. Machamp and other fighting types make short work of Snorlax, but have to be wary of that 110 base attack as well as possible paralysis from Body Slam."
If anybody ended up reading all that, congrats. I feel that the stuff near the top of this post wasn't as good as most of the stuff I wrote in the middle, but I can't say that I'm a good impartial judge when it comes to my own writing.
