[Naix]

So I finished my Red playthrough (which took far longer than it should have), and here are the entries for the Pokemon I used. If anything seems off, please say so.

Jigglypuff

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Jigglypuff - Low Tier
-Availability: You can catch it at Route 3 in Red and Blue, at levels 3, 5, and 7. In Yellow, you have to wait until you get to Route 5. It evolves by using a Moon Stone, which can be obtained shortly after catching Jigglypuff.
-Stats: The only stat that can be considered "good" is HP, which is actually a curse in disguise, as if it has low health, it'll take more items to heal it than others. It's also one of those Pokemon that are actually outsped by some of the non-boss trainers' Pokemon.
-Movepool: Considering its only move before reaching level 9 is Sing, it needs Water Gun and/or Mega Punch to actually fight. Also, aside from Rest and Body Slam at levels 29 and 34, respectively, its level-up movepool is absolutely barren, thus requiring the use of even more TMs for it to try to keep up.
-Power: If you evolved it ASAP (which you should have) and taught it Mega Punch, it's actually pretty decent. Then you reach Rock Tunnel, and it can't do much in there unless you taught it Water Gun/BubbleBeam/Seismic Toss, and it has trouble in Pokemon Tower no matter what you taught it. The Poison-types of Cycling Road and Silph are also a pain unless you taught it Psychic. To make a long story short, Wigglytuff needs TMs to be usable for at least half of the game.
-Type: Normal has no type advantages against anything else, not even Ghost because the only Ghost-type move that won't affect Normal-types is the pathetic Lick. The fact that Normal-types don't hit anything super-effectively balances out how uncommon Fighting-types are in-game.
-Match-ups:
--Misty: An interesting trick against Misty that actually works: Before fighting her, make sure Wigglytuff knows Mega Punch and Bide. Then, when fighting her, defeat Staryu normally, with Mega Punch. After that, use Bide. Wigglytuff's bulk should allow it to take 4 BubbleBeams (barring crits, of course), and if it loses at least 30 HP, its Bide will be strong enough to OHKO Starmie.
--Lt. Surge: Wigglytuff can take a Thunderbolt from Raichu, but not much else on top of it.
--Erika: You'll get Wrapped up when fighting Victreebel. It can beat her other Pokemon, but only if you taught it Ice Beam or Psychic.
--Koga: In Red and Blue, his Pokemon are physically defensive juggernauts, all of which take minor damage from Strength, and in Yellow, they all know some sort of status move. Keep in mind that his Pokemon are most likely faster than Wigglytuff.
--Sabrina: Wigglytuff can defeat her Kadabra if it knows Body Slam and manages to paralyze it. For the others, it has to hope they use Psywave instead of Psybeam/Psychic.
--Blaine: Fire Blast is going to do a lot, regardless of who's using it. Don't forget that Ninetales (Yellow only) and Rapidash know Fire Spin. Also, Arcanine can actually survive 2 uses of Strength.
--Giovanni: Wigglytuff needs Ice Beam or Blizzard for this fight, or else it's going to be walled. The sad thing is, his Nidos, Dugtrio, and Persian are all faster than Wiggs, and of those, Dugtrio's the only one that can't withstand a Blizzard.
--Lorelei: Thunderbolt is required here, as 3 of her Pokemon have great physical bulk, and Dewgong (obviously not one of the above 3) has Rest. Of course, Thunderbolt has trouble 2HKOing the majority of her team, all of which (minus Slowbro) are faster than it, meaning it'll most likely take at least 3 hits from each mon.
--Bruno: I don't think any explanation as to how Bruno defeats Wigglytuff is necessary.
--Agatha: If Wigglytuff has a hard time in Pokemon Tower, how well do you honestly think it'll do against Agatha?
--Lance: It's a sad day when a Thunderbolt fails to even 2HKO a Gyarados. Same goes for Blizzard and everything else on his team, except for Aerodactyl and Dragonite. Thankfully, Wigglytuff has just enough bulk to survive a Hyper Beam from anything not named Gyarados or Dragonite.
--Rival: It needs TMs to do well against any of his Pokemon, with the exceptions of Exeggutor, which is the worst Pokemon on his team, and his Alakazam and starter, which can't be beaten regardless of what you taught Wigglytuff. Ninetales also poses a serious threat, thanks to Fire Spin.
-Additional Comments: Third worst Pokemon in the game, right here. Jigglypuff is comparable to a parasite, as they both rob you of important things (exclusive TMs for the former, nutrients for the latter) and weaken your performance overall. Thankfully, Jigglypuff is easier to get rid of than a parasite, and the way do do so is as follows:
Step 1: Deposit Jigglypuff/Wigglytuff.
Step 2: Release Jigglypuff/Wigglytuff.
That's pretty much all you need to know about Jigglypuff.

Mankey

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Mankey (unavailable in Blue) - Mid Tier
-Availability: In Yellow, you can find it as early as Route 22, while in Red, you'll have to wait until Route 5, where it can be found at levels 10, 12, 14, and 16. It evolves at level 28, which is rather late for a Pokemon that only evolves once.
-Stats: Standard combination of good Speed and Attack, even though it's somewhat lacking for the latter. Admittedly, its Speed could be considered overkill, considering the fact that Karate Chop, its main move, crits all of the time.
-Movepool: In terms of level-up moves, it doesn't really gain much of note outside of Low Kick (Yellow only) and Karate Chop. For TMs, it greatly appreciates Dig to hit Poison-types. It's also one of the few Pokemon that can learn and make good use of Rock Slide. Believe it or not, Submission, its best STAB, is actually not as good as you might think, because despite the fact that it nabs several KOes Karate Chop can't, its 80% accuracy combined with its 1/3 recoil.
-Power: Mankey's between a rock and a hard place here, as unless it's using Submission (which makes its frailty even more noticable), its neutral hits just barely miss out on OHKOing its opponents, even after evolving. This holds true for the entire game.
-Type: Fighting is resisted by the majority of Pokemon in the game, and the lack of a secondary type doesn't exactly help it in that regard.
-Match-ups:
--Brock: He is swept, thanks to Low Kick.
--Misty: Mankey's just too frail to stand up to Starmie.
--Lt. Surge: Victory or loss agaist Lt. Surge in Red depends on whether you taught Mankey Dig or not. However, in Yellow, Raichu outspeeds Mankey and OHKOes it.
--Erika: Primeape can beat either Vileplume or Victreebel, but not both. It beats Tangela no matter what.
--Koga: In Red, all of his Pokemon are able to stomach a Dig and strike back with Sludge or Selfdestruct, and in Yellow, his entire team knows Psychic.
--Sabrina: Primeape's fast enough to get the first swing in, but can't OHKO any of her Pokemon. It then gets OHKOed with Psybeam or Psychic. At least it can beat Mr. Mime and Venomoth.
--Blaine: Fire Blast and Take Down both hurt, but if Primeape knows Dig (which it should if you're using it), it can beat all of his Pokemon, save for Arcanine.
--Giovanni: All of his Pokemon (except for Persian) can withstand a Submission and strike back with Earthquake/Thunder/Body Slam.
--Lorelei: Dewgong will spam Rest even if it's at full health because it's a Psychic-type move, allowing Primeape to beat it easily. The same applies for Slowbro and Amnesia, but it's easily more durable, taking as much damage from Karate Chop as a Super Potion heals, leading to a stalemate. It can also beat Jynx and Cloyster, but has trouble with Lapras.
--Bruno: This is an uncommon scenario: one where Hitmonchan is actually threatening. The reason? Counter. If you use any attacking move not called Rock Slide or Dig on Hitmonchan, it can Counter it and most likely KO Primeape. Hitmonlee's and Machamp's attacks also hurt.
--Agatha: This battle is a lost cause if Primeape doesn't know Dig, but with Dig, she is swept, save for Golbat, who can be crushed by Rock Slide.
--Lance: In Red, his Dragonair and Dragonite know non-damaging Psychic-type attacks, allowing Primeape to beat them without taking any damage. In Yellow, however, Lance's entire team becomes much more threatening, and Primeape can only beat the Dragonair.
--Rival: Alakazam and the starter always win against Primeape, while the rest of his team has varying levels of easiness (Gyarados = no dice, Pidgeot, Ninetales, Cloyster, and Sandslash are risky but doable, Rhydon and Exeggutor don't stand much of a chance).
-Additional Comments: Mankey is a poor man's Sandshrew, seeing as how it's weaker, frailer, and evolves later. Despite this, Mankey is definitely usable and has potential to be good, albeit at the price of Dig and possibly Rock Slide.

Scyther

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Scyther (unavailable in Blue) - Low Tier
-Availability: There are 2 ways to get a Scyther, and neither of them are pretty. The less expensive but also less recommended way is by looking for it in the Safari Zone. Keep in mind that it's a 4% encounter at best, and they tend to run away after one turn. The recommended but far more expensive method is to spend 110,000 poke (130,000 in Yellow) at the Game Corner. Regardless of the method, it'll be at level 25 (or close to it) when you get it.
-Stats: It has good Attack and great Speed. It also has enough bulk to take a few neutral physical hits.
-Movepool: Scyther's movepool is disappointingly shallow, outside of Slash (which it learns at level 29). It learns Swords Dance and Agility, but it never has a use for either of them, as Slash's omnipresent criticals negate the attack boosts from Swords Dance and Scyther's already faster than almost everything already, making Agility useless. Also, its attacking movepool is composed entirely of Normal-type attacks, with the exception of Wing Attack in Yellow, but Scyther doesn't learn it until level 50, and it's so weak that the only thing it hits harder than Slash is Ghost-types, which are in only one battle in the game by the time Scyther might have learned it.
-Power: By the time you get it (assuming you played the game normally), you'll be at Pokemon Tower, where the majority of enemies happen to be Ghost-types, which wall Scyther better than *insert food of your choice here* tastes. Assuming you chose to go to Cycling Road first, Scyther's going to have a very rough time catching up thanks to seemingly everybody there having a Poison-type with good Defense. Also, even with Slash, it still has a bit of trouble OHKOing Pokemon that have decent Defense.
-Typing: With everything else it has in mind, Scyther really would've appreciated if it was at least part Normal-type, so it would get STAB from Slash. Instead, it gets no STAB whatsoever (if you say Wing Attack...) as well as a weakness to Poison-type attacks. At least it isn't part Grass-type...
-Match-ups: Note: All of the following are assuming Scyther knows Slash, as its capabilities are quite feeble without it.
--Lt. Surge: His team is swept in Red, but Raichu can occasionally survive a Slash in Yellow thanks to its higher level and then proceed to OHKO with Thunderbolt.
--Erika: Scyther's faster than her team, making Wrap not as threatening as it would've been (unless of course Scyther got paralyzed prior to the fight), and it has a 4x resistance to Grass-type moves.
--Koga: Considering Scyther's weak to Poison-type attacks and Slash failing to 2HKO Koffing, things won't go well for it in Red. In Yellow, it has a better chance, and might be able to take down more than one of his Pokemon, assuming none of them use Stun Spore or Sleep Powder.
--Sabrina: Her entire team is outsped, and Kadabra and Mr. Mime are flat out OHKOed by Slash. Venomoth and Alakazam can both survive one Slash, but they need to use Psybeam and Psychic to beat Scyther. In Yellow, Scyther loses the Speed advantage and the ability to OHKO Kadabra, because of it being higher levelled.
--Blaine: Every member of his team knows Fire Blast, and as such I feel no need to explain what the outcome of this battle might be.
--Giovanni: His Rhyhorn/don wall Scyther, and the Nidos have enough bulk to take a Slash. In the transition from Red to Yellow, there's good news and bad news: the good news it that he got rid of his Rhyhorn and Dugtrio can no longer touch Scyther. The bad news is that Persian can do more to you than Rhyhorn can, and the Nidos learned Thunder.
--Lorelei: All of her Pokemon (barring Jynx, who is outsped and OHKOed) fit at least 1 of 2 criteria:
1. Can take repeated Slashes.
2. Know an Ice-type move of some sort.
--Bruno: This battle features a double rarity: His Onix actually holding their own against something, and Hitmonchan being genuinely threatening (thanks, Counter!).
--Agatha: Nothing doing.
--Lance: Hyper Beam does a chunk regardless of who's using it, and Scyther has trouble 2HKOing anything on his team. In Yellow, things are even more hostile, as all of his Pokemon, with the exception of Gyarados, know super-effective moves.
--Rival: First of all, make a list of every Pokemon he'll use when you fight him. Then, cross out anything that's faster than Scyther, are physically bulky, or have a type advantage. The remaining Pokemon on the list should be Exeggutor and Venusaur, as while Blastoise and Vaporeon don't completely meet any of the above categories, keep in mind that they know Ice-type attacks.
-Additional Comments: Scyther is the closest thing to a one-trick pony in RBY; it has Slash, but nothing else. It's also one of the most expensive Pokemon in the game, second only to Porygon, and when all you get from 5500 coins is a Pokemon which has only one good move (which has absolutely no super-effective coverage), something's wrong.

I'll write up the other entries when I have enough free time.