039 - Jigglypuff
Normal/Fairy (Normal Prior Gen VI)
Jigglypuff can be seen as a "counterpart" to Clefairy, as they were both introduced as magical Normal-type Pokemon in Generation I who evolved with the Moon Stone, and received a Baby in Generation II. While Clefairy in Generation VI became pure-Fairy, Jigglypuff instead kept its Normal-typing alongside gaining the Fairy-type. Personally, I don't get why Game Freak didn't make Jigglypuff pure Fairy-type as well since the two Pokemon had always been similar, but that's what Game Freak ended up doing!
Jigglypuff is a round, pinkish Pokemon who brings to mind Nintendo's own Kirby due to its ability to inflate its body like a balloon. One oddity about Jigglypuff's appearance is that in the games, it tends to have a darker pink color and blue eyes while in the show and Smash Brothers (until Smash 4 went with the game's coloring), its appearance was much lighter and it had green eyes. Game Freak seemed to homage this in Jigglypuff's Shiny introduced in Generation II, which greatly resembles its anime incarnation, so much so that some people speculate that the anime's Jigglypuff was always intended to be a Shiny Pokemon. This was proven false, however, as subsequent Jigglypuff in the show all used the lighter color scheme.
Like Clefairy, Jigglypuff evolves through the use of the Moon Stone, but its connection to the Moon isn't as strong as Clefairy---one episode of the show hinted that Clefairy had a relationship with Jigglypuff, but otherwise the games don't imply Jiggs to have an extraterrestrial origin like they do with Clefairy. Jigglypuff's body-shape, however, does resemble the moon, as does its saucer-shaped eyes, so it evolving with the Moon Stone feels natural and expected.
In Japan, Jigglypuff is called the Japanese term for pudding, "purin", but it doesn't seem to actually be made of pudding or edible. Its American name somewhat keeps this food theme in-tact, as the "puff" brings to mind the Jet-Puffed Marshmallow brand (or, more likely, the fictitious Stay-Puft brand featured in Ghost Busters), and its pre-evolution is even described to have a body that feels like a marshmallow. A later Fairy-type Pokemon introduced in Gen VI that resembles a popular food item makes me think that Pokemon based on confectionery sweets might become a reoccurring theme when it comes to designing Fairy Pokemon, something that honestly I'm all for.
Jigglypuff's trademark ability, even more iconic than its ability to inflate itself, is Sing. This primarily gained popularity thanks to the television show, but was Jigglypuff's signature move in the games as well, and the sound effect used in the games became the basis for "Jigglypuff's Lullaby". Sapphire's PokeDex introduces a rather dark element to it, though---Jigglypuff doesn't breathe when it's singing, and will possibly suffocate itself when singing for an opponent it cannot put to sleep.
While never on the level of Pikachu, Jigglypuff became quite popular due to its appearance in Super Smash 64 as one of the game's four secret characters. When it comes to the Pokemon Franchise, it's been said that The Pokemon Company has a say in what Pokemon Sakurai includes, and Jigglypuff was probably put in due to being a very popular Pokemon thanks to the show---in fact more than any other franchise in Smash Brothers, Pokemon seems to draw the most from its expanded media than it does the main games. Jigglypuff was a "joke character", but could be potentially lethal when used correctly, it's apparently pointless Rest move capable of delivering a powerful hit if used when right on top of the opponent. As Jigglypuff's popularity waned in favor of newer Pokemon, some fans have expressed surprise that Jigglypuff has returned for every Smash sequel, but that's probably because it was one of the original 12, and it could be said to be an iconic Smash Brother at this point more so than it is an iconic Pokemon. Like with Captain Falcon, Jigglypuff's Smash Brothers' appearance is basically its main draw at this point. I imagine if Jigglypuff was ever dropped, the outcry would be huge.
In the show, Jigglypuff was a reoccurring character during the earlier seasons, following Ash and co. throughout their adventure. Unlike Jigglypuff in the games, who are said to Sing with the intent of putting their foes to sleep, this Jigglypuff actually wanted to have someone listen to its song, which, as expected, always failed resulting in it getting angry and using its microphone/marker to doodle over everyone's face before storming off. In its last appearance in Hoenn, it finally accomplished this thanks to a Whismur's Soundproof Ability---but even Whismur couldn't help but fall asleep at the end of the episode, worn out by that day's adventures. Jigglypuff marched off, but this time was never seen again---except for a small cameo in one of Best Wish's endings alongside other mascot Pokemon from throughout the show's run. You know, I'm surprised they never let one of the characters actually catch Jigglypuff. It would've fit quite well with May and her Contest Adventures. Outside of the main Jigglypuff, a giant one appeared in the Ancient Puzzle of Pokemopolis, and as the focus on an early Battle Frontier filler which was another instance of Battle Frontier ignoring a well-established character in favor of a cheap replacement.
040 - Wigglytuff
Normal/Fairy (Normal Prior Gen VI)
Wigglytuff is the evolved form of Jigglypuff, and loses its spherical shape in favor of a "jelly-bean" shape as well as grows long, rabbit-like ears. Given that rabbits in Japan have a connection to the moon, I imagine this element of its design was done to help signify it evolving through the use of a Moon Stone. In older art, Wigglytuff's mouth was above its white belly, but in modern appearances its mouth is now placed right at the top of its belly instead. Like Jigglypuff, its colors in the game were darker than how it appeared elsewhere, although as it didn't appear as frequently as Jigglypuff this wasn't as noticeable.
While Jigglypuff focused on its Sing ability, Wigglytuff instead focuses more-so on its ability to inflate itself just like a balloon. It does this as a means of intimidation, and the PokeDex gives off the impression that Wigglytuff is somewhat of a mean Pokemon who's quick to anger despite its cuddly appearance. Unlike Sing, the ability to inflate has yet to have a move that really represents that ability---I always thought a move that worked akin to Magnet Rise, but for Pokemon who could inflate themselves, would be a fitting idea.
Wigglytuff had a rather memorable appearance in the Pokemon Mystery Dungeon Explorers series, as the leader of the Treasure Town guild the player belongs to. Despite his cute and childish nature, Wigglytuff is shown to be an extremely powerful and frightening Pokemon when angered. You'd never think a Pokemon like Wigglytuff could be such a badass!
In the show, Wigglytuff first appeared in a somewhat meta-episode all about making a Pokemon Movie that aired around the release of Pokemon: The Movie. This episode seemed to support the idea that Wigglytuff is actually somewhat of a cruel Pokemon, as it had a very diva-like attitude to it and was very hard to work with. It played the role of a Juliet-type character opposite Misty's Psyduck in the Romeo role. In Hoenn, May's rival Harley used a Wigglytuff who was depicted as extremely vicious and cruel-hearted. Some fans I recall speculated that this was THE Jigglypuff last seen in an earlier Hoenn episode, but there's nothing to support this since we don't see its trademark microphone or Sing ability. Wigglytuff has recently gained prominence in the XY series where due to its new Fairy Type making it marketable again, is now depicted as Nurse Joy's signature Pokemon in Kalos as opposed to the traditional Chansey. It mainly plays a background role, but there's been a focus episode on one of these Wigglytuff nurses.
174 - Igglybuff
Normal/Fairy (Normal Prior Gen VI)
Like Pichu and Cleffa, Igglybuff is another example of a Baby Pokemon created with the sole-goal of being cute and marketable. Despite this being the goal, both Cleffa and Igglybuff never really took off, and their evolutions tend to be more well-known and beloved than they are. Its dub name is a bit odd to me---there's not really any other options to keep the rhyme going (duff? fuff?), but "buff" was an odd choice since the Pokemon is anything but buff.
Igglybuff is also known as the Balloon Pokemon, and the little knot on its head somewhat resembles the bottom portion of a balloon that you tie the string around. Going by the PokeDex, Igglybuff's body is a bit different from Jigglypuff and Wigglytuff, as it's described as being more like a bouncing ball than a balloon. It's also said to not be as good at singing as Jigglypuff due to its weaker vocal cords, but of course in the games its Sing attack is just as effective as its evolutions. The most notable difference compared to its evolutions though are its bright, red eyes---perhaps meant to represent a Red Moon?
In Pokemon Mystery Dungeon Explorers of Sky, the "third version" of the Explorers series, Guild Master Wigglytuff was given a special Side Episode where you played as him during his days as an Igglybuff showing his backstory and his journey to become a top-notch Explorer. Per the Mystery Dungeon games, this involves a surprisingly touching plot involving a morally ambiguous mentor.
Igglybuff had like one "major" appearance in a Johto filler as a dance-group duo who had a rivalry with Jigglypuff, but I barely remember anything about that episode. Otherwise it's played bite-size roles.