Trainer Classes that focus on typeless categories

Bird Keeper -Focuses on bird-based Pokémon.
Scientist: Focuses on artificial Pokémon and humanoid Psychics.
Hex Maniac: Magical Pokémon, ie. Ghost and Psychic.
Guitarist: Sound-based Pokémon.
Fisherman: Focuses on fish-based Pokémon.
Scuba Diver, Free Diver: Uses deep sea Pokémon.
Beauty: Cute and beautiful Pokémon.
Poké Fan: Cute Pokémon, primarily Fairy Egg Group and Baby Pokémon.
Sightseer :Typical variant of a regional variant.

Ace Trainers and their variants, and regular human trainers(Fans, sportspeople etc.) are not listed.

Honorable mentions:

Super Nerd: Generally uses a Fire, Poison and Electric Pokémon, but also prefers synthetic Pokémon.

Trainer Classes according to types:

Bug-type specialists:
Bug Catcher: Ever-present in Japanese based regions, but doesn't appear in Western regions.
Bug Maniac: Hoenn exclusive.
Bug Catching Man: PBR exclusive

Dark-type specialists:
Delinquent: OR/AS exclusive
Roughneck: Doesn't appear in Hoenn and Kalos
Street Thug: OR/AS exclusive

Dragon-type specialists:
Dragon Tamer: Exclusive to Sinnoh and Hoenn.

Electric-type specialists:
Cameraman: Sinnoh exclusive.
Cyclist: Exclusive to Sinnoh and Unova.
Electrifying Guy: PBR exclusive
Engineer: Kanto exclusive
Guitarist: Doesn't appear in Kanto and Kalos
Poké-Kid: Sinnoh exclusive
Rocker: Kanto exclusive
Shocking Girl: PBR exclusive
Super Nerd: Kanto and Johto exclusive
Triathlete(Biker): Hoenn exclusive

Fairy-type specialists:
Fairy Tale Girl: Kalos and Hoenn exclusive
Furisode Girl: Kalos exclusive

Fighting-type specialists:
Battle Girl: Doesn't appear in Kanto and Johto
Black Belt: Everpresent.
Crush Girl: FR/LG exclusive
Crush Kin: FR/LG exclusive
Expert: Hoenn exclusive
Hiker: Everpresent
Linebacker: Unova exclusive.
Old Couple: Hoenn exclusive
Roughneck: Doesn't appear in Hoenn and Kalos
Sailor: Japanese regions only.

Fire-type specialists:
Burglar: Kanto and Johto exclusive
Cyclist: Exclusive to Sinnoh and Unova.
Firebreather: Johto exclusive
Kindler: Hoenn exclusive
Super Nerd: Kanto and Johto exclusive

Flying-type specialists:
Cyclist: Exclusive to Sinnoh and Unova.
Bird Keeper: Japanese regions only
Golfer: Alolan exclusive
Pilot: Unova only.
Sky Trainer: Kalos only.

Ghost-type specialists:
Channeler: Kanto exclusive
Hex Maniac: Hoenn and Kalos exclusive.
Medium: Johto exclusive

Grass-type specialists:
Aroma Lady: Hoenn and Sinnoh exclusive.
Pokémon Ranger: Doesn't appear in Kanto(besides Sevii Islands) and Johto.

Ground-type specialists:
Hiker: Everpresent
Muddy Boy: PBR exclusive
Pokémon Ranger: Doesn't appear in Kanto(besides Sevii Islands), Kalos, Unova and Johto.

Ice-type specialists:
Boarder: Johto exclusive
Cool Beauty: PBR exclusive
Icy Guy: PBR exclusive
Skier: Exclusive to Johto, and Sinnoh.

Normal-type specialists:
Painter: FR/LG exclusive
Tuber: Doesn't appear in Unova, Kalos and Kanto besides Sevii Islands.

Poison-type specialists:
Biker: Doesn't appear in Kalos, Hoenn and Sinnoh
Janitor: Unova exclusive
Ninja Boy: Hoenn and Sinnoh exclusive.
Super Nerd: Kanto and Johto exclusive

Psychic-type specialists:
Clown: Sinnoh exclusive
Hex Maniac: Hoenn and Kalos exclusive.
Psychic: Everpresent

Rock-type specialists:
Hiker: Everpresent

Steel-type specialists:
Steel Spirit: PBR exclusive

Water-type specialists:
Fisherman: Everpresent
Free Diver: OR/AS exclusive
Navigator: XD exclusive.
Sailor: Japanese regions only.
Scube Diver: OR/AS exclusive
Sis and Bro: Hoenn and Sevii Islands exclusive
Surfer: Alola exclusive.
Swimmer: Everpresent
Swimming Club Member: PBR exclusive
Triathlete (swimmer): Hoenn exclusive
Tuber: Doesn't appear in Unova, Kalos and Kanto besides Sevii Islands.

Edit(29.03.2018): Added USUM additions.

Let's discuss fan types. Part 8. Cyber/Digital/Virtual-type

1. So, what is this type all about?
A fairly recently conceived type, Cyber-type expects to include the new technological advancements of modern computer science within the Pokémon universe.

This type includes computer software and technological species that can't be presented as Steel or Electric, either because they must have another type, or are completely made of data and merely have physical projections within the magical nature of Pokémon universe.

2.Where does this name come from?

The type does not have a determined name, because of its vague nature as a concept.

3. Does this type have an in-game source?

Yes, the Porygon-line and to lesser extent Genesect embody the concepts behind this type.

Porygon-line are entirely software based species, with moves like Conversion and Conversion 2, which refer to Conversion of a file type from one type to another. Their Japanese name is Texture, and Texture 2, which refer to the Texture of 3D models.

Techno Blast is move caused by Genesect's Megelo Cannon and Genesect are cybernetic Pokémon, enhanced with mechanic parts.

The ability Download is purely software based.

4. What would be the ideas behind such a type?

Primarily this type would include virtual software and artificial intelligence, as well as possibly cyborgs.

Whatever the type might be, it must be related to computer science.

5. What would be the type interactions of such a type?

It is hard to say. Certain stuff based on short circuiting and other machine errors must be considered.

6. What would be the distribution of such a type?

Definitely low. The only possible way this type can be common is if the species are purchased through man-made means, much like how Porygon is a game prize. Another way would be to introduce a cyberspace, a concept invented during the 90s that falsely believes the information change processes of computers exist within a completely different universe within our own, similar to how one's mind emerges due to interaction of neurons. This idea was actually used by GameFreak with the action platform game Pulseman.

 7. Future comments:

The whole idea behind this is to further demarcate Normal-type, by getting rid of its status as an encompassing type that includes anything that can't be any of the other existing types.

Something similar to this might happen for Bird based, Animal based, or cell based Pokémon within Normal-types, but I'm not sure if I'll discuss such ideas. 

This idea is also problematic because it is too similar to Pokémon's primary rival, Digimon.

Should Cacophony be brought back?

Cacophony, whose Japanese name translates to Noise, was an ability introduced in Generation III, but was ultimately removed. This ability was intended to be a counterpart, if not the original version of, Soundproof.

What are the differences between Soundproof and Cacophony?

The fundamental difference between Cacophony and Soundproof is the ideas behind each ability.

Cacophony manages to block Sound based moves due to loud noise generated by its user, which is how Whismur-line blocks sound:

Sapphire: Loudred shouts while stamping its feet. After it finishes shouting, this Pokémon becomes incapable of hearing anything for a while. This is considered to be a weak point.

However, all the other species that get Soundproof either have massive armor that blocks sound(Shieldon-line) or are incapable of hearing because they lack ears(Mr. Mime, Electrode etc.)

This creates a logical contradiction, as Exploud-line is perfectly capable of communication with others:

Sapphire Exploud communicates its feelings to others by emitting whistle-like sounds from the tubes of its body. This Pokémon only raises its voice when it is in battle.

which doesn't make sense if it is incapable of hearing.

While it is true that Whismur-line seems to have a biological mechanism for blocking out sounds, other Sound based species who don't have such a mechanism are rendered incapable of blocking Sounds.

What advantage would Cacophony bring?

Cacophony, if it is brought back, could be obtained by Sound-based Pokémon, such as Chatot, Jigglypuff, Kricketune, Woobat, as a means of blocking Sound based moves.

Conversely, Soundproof could evolve into an ability that includes other methods of blocking sounds.

Perhaps more interestingly, if Cacophony is brought back, it could be obtained by certain moves similar to how Worry Seed induces Insomnia. For example, Uproar can temporarily transform its user's ability to Cacophony.

Is it likely that this will happen?

Probably not, since the current repertoire of Sound-based moves are either weak, exclusively Normal-type or rare.

Let's discuss fan types. Part 7. Light-type

1. So, what is this type all about?
Light-type is one of the most commonly discussed fan-types. The reason is obvious. The presence of Dark-type without a proper counterpart, in spite of attempts by Psychic and now Fairy, has always been a cause of speculation due to dualistic nature of Western philosophy post-Plato.

Light-type is also fairly persistent due to excessive non-presence of Western thought, particularly Abrahamic religions and different philosophies inspired by them.

2.Where does this name come from?

The name comes from the TCG deck Light, and Light Pokémon section in TCG.

3. Does this type have an in-game source?

Yes and no. There has been some abilities and moves related to Light and religious philosophy, but they are completely sporadic.

Most, but not all, of the Light Pokémon from TCG are now part-Fairy.

4. What would be the ideas behind such a type?

The discussion can be found here. Generally speaking, Light is thought in two manners:

1. Light as photons, and other scientific phenomena.
2. Light as metaphor for good and divine.

My personal favourite is 1, since I believe the second can be its own type, as a Holy/Aether-type.

Best depiction of Light-type I have seen so far is from Koino Region.

5. What would be the type interactions of such a type?

It depends on the idea behind it. If it is metaphorical, then its interactions would be based off paranormal types.

If it is scientific, then Grass and Ice will get moves that they can resist or be immune to.

6. What would be the distribution of such a type?

If it is metaphorical, then it would be very rare, probably, unless petty altruism is allowed to be in Light-type, much like how petty villainy is part of Dark-type.

If it is scientific, then it will get several different Pokémon, particularly a lot of Pokémon would be converted to it.

7. Future comments:

Since Fairy currently attempts to be the Light-type, we will likely not see Light-type in near future. But since Fairy will almost certainly fail to deliver due to its association with Paganism and Mythology.

But if GF wants to go with scientific depiction of Light-type, then a Light-type can be created at any time, at least when we have enough Light-based Pokémon and moves.

Let's discuss fan types. Part 6, Crystal-type

1. So, what is this type all about?

This type largely originates from two elements, the Crystal Onix from the Orange Islands arc of the Original Pokémon animé series:

The second origin is the Crystal-type in TCG. In TCG, this type is a Poké-Body, which allows Colorless Pokémon to temporarily get another TCG type if they have that type's Energy card.

The primary inspiration behind this type is the general failure of Rock-type, particularly when it comes to showcase different rock types besides volcanic rocks, such as granite or magnetic rocks. As such, the only Rock-types that have crystals on them are Carbink and Diancie, whereas there are several Pokémon from other types with crystals on them, particularly in Psychic.

2.Where does this name come from?

See above.

3. Does this type have an in-game source?

Sort of. Both Power Gem and Diamond Storm are based off crystals, and are learned by Pokémon who have or composed of crystals.

The Crystal-type in TCG is also an inspiration.

4. What would be the ideas behind such a type?

There are three concepts this type can use;

1. Crystals as a general notion for all jewels. So, in this case, ambers and pearls can also be considered "crystals", so could gold and silver.

2. Scientific depictions of crystals, which is immensely rich.

3. Crystals as mystical power sources, which would be primarily inspired by the concept of crystal healing and depictions of crystals in JRPGs such as Final Fantasy.

5. What would be the type interactions of such a type?

Crystal as a type on its own is speculated here and here.

Crystal as a pseudo-type is characterized in Pokémon Azurite, where Crystal is a form-exclusive type that has no type interaction besides having STAB.

6. What would be the distribution of such a type?

Probably very rare, if it is created to be a powerful mystical type, or uncommon, if it is closer to Steel-type.

7. Future comments:

Because Rock-type does not have any major subsection of Crystal-based Pokémon, and all crystal based Pokémon are better off with other types besides maybe some Ice-types, this type has low chance to be conceptualized in near future, unless a radical amount of Crystal Pokémon is announced, a la Dark-type.

Let's discuss fan types. Part 5, Wind/Air-type

Sauce.
1. So, what is this type all about?

This type is born out of the vacuum of a proper wind and air based type, and air's presence in most classical elemental hierarchies. 

This idea generally exists because the default air based type, Flying, is primarily based on species that can fly, rather than manipulation of air. This is because Flying-type's original version was Bird-type, which was untenable due to presence of Flying non-bird Pokémon such as Butterfree and Zubat-line.

2. Where does this name come from?

The name primarily comes from Final Fantasy elemental type, Wind.

The name Air comes from the four classical elements, fire, air, water and earth.

3.Does this type have an in-game source?

Yes, as a subsection of Flying.

Flying encompasses four major elements:

Acrobatics related moves such as Acrobatics.

Air manipulation based moves such as Gust, Hurricane, Air Cutter, Air Slash, Tailwind.

Bird based moves such as Sky Attack(Jp. name: God Bird), Aerial Ace(Jp. name: Swallow Cut) etc.

Flying based moves such as Fly, Bounce etc.

The second major element is what Wind-type is expecting to expand.

Other wind based moves such as Fairy Wind, Whirlwind(Japanese name: Blow Away) and Ominous Wind exist in other types. 

4. What would be the ideas behind such a type?

Final Fantasy's Wind element is a good reference. Air's status as one of the classical elements and its associations can also be used.

Wind's current scientific understanding can be used as well.

5. What would be the type interactions of such a type?

Primarily similar to Flying, but association with biological elements might not be present. For example, Ice and Electric weakness are meaningless for Wind, since Wind Pokémon will not be Flying animals, but probably wind spirits and such. Conversely, super-effectiveness against Bug would be meaningless because unlike bats and birds Wind-based Pokémon would likely not eat Bugs.

6. What would be the distribution of such a type?

Most likely, it would be similar to Fire and Electric, present in all regions in earlier routes, but relatively rare in both the amount of species and amount of locales they are available.

7. Future comments:

If such a type is created, Flying-type must have a new paradigm for Special moves. Chatter and Oblivion Wing are both wind independent special Flying moves, but both are signature moves based on abilities of bird Pokémon.

Something more commonly presentable must exist to fill the void that will be created by the introduction of a wind-type.

Editor's note: I don't personally like this idea, but this is a very popular one, and I can't really think of a means of introducing weather based and wind based phenomena, or classical interpretations of air with mysticism with Flying.
I can, however, definitely imagine such concepts being introduced within the limits of a Flying-type, something like say, a wind demon with regular wings. But I can't think of a wind demon that only manipulates air in Flying-type.

Edit(12.06.2021): Fixed Ominous Wind to Oblivion Wing.

Let's discuss fan types. Part 4, Cosmic/Alien-type

1. So, what is this type all about?

Cosmic-type is a fairly recently thought of type that emerged out of the vacuum for a dedicated type for extraterrestrial Pokémon, and their default setting as Psychic-type.

The earliest this idea can be traced is this deviantart blog, though idea likely predates that.
This is also called the "Alien-type".

2. Where does this name come from?

The name "Cosmic" comes from Cosmic Power, a Psychic-type move that is available for almost all extraterrestrial Pokémon.

Much like Magic, this idea is largely popularized due to Gymjack's image, but it is also often discussed on 4chan.

3.Does this type have an in-game source?

Yes, again, largely as a subsection of Psychic.

Gravity and Cosmic Power are space related Psychic-type moves, and several Psychic Pokémon and Cleffa line are extraterrestrial  Pokémon.

This is largely due to influence of Mother series, where alien species are known to use PSI moves(psychic attacks).

4. What would be the ideas behind such a type?

The general assumption is that a Cosmic-type would include moves related to extraterrestrial objects and creatures, primarily relying on modern day cosmology and science-fiction tropes for aliens.

It is possible that such a type might also include previous mythological approaches to extraterrestrial elements, but it is likely that such elements will fit better with paranormal types (Fairy, Psychic, Dragon etc.)

Another aspect of such a type would be the use of modern day large object physics, such as gravity, time travel through black holes, general theory of relativity etc.

5. What would be the type interactions of such a type?

It is hard to say, it can be immensely defensive or immensely offensive. Whatever it is, it will likely be based off difficulties of living in space.

6. What would be the distribution of such a type?

While Pokémon that mess with basic physics can be common, primary extraterrestrial Pokémon, just like current alien Pokémon, would be relatively rare.

This makes sense, considering how hard it is to survive in outer space for earth-evolved species like us, and space related mass extinction events and general rarity of UFO rumors.

7. Future comments:

The primary purpose of such a type would be to help relatively weak extraterrestrial Pokémon to have their niche, and introduce a lot of fringe theories about aliens to Pokémon franchise.