Self-Imposed Challenge/Pokémon

The Pokémon franchise has such big playerbase, and due to the age of the franchise and the gameplay structure of its core games, it's natural that a lot of Challenge Gamers would arise to make their own Self-Imposed Challenges and share it with everyone.

The Core Games[]

Some of the more generic examples include the Monotype (using only Pokemon of a certain Type), One-Poke, No Evolutions, Speedruns, Scramble (other players picked your team for you), No Recovery Items, or No Pokémon Center runs.
Try the Perma Death run, which came in two flavors: The first variation has rules in which if a Pokemon faints, it gets released/boxed. And the second one (also called the No-Whiteout challenge) have it that if all of your Pokemon in the party faint, it's Game Over and you have to start a new file.
There are also several minor challenges that limit what you can do to an equal to similar level as NPC Trainers could, such as challenging Gym Leaders and/or the Elite Four with the same amount of party members, or only using one or two recovery Items during the battle.
There's also the infamous "Nuzlocke Challenge", named after the comic of the mode's creator. This challenge is also usually mixed in with other challenges to add a layer of difficulty/variation. The core rules are pretty simple:
- All faintings are permanent (either via releasing the fainted Pokemon or just boxing them) until your run ended.
- You're only allowed to catch the first pokemon you encounter in the wild. Shiny Pokemon or Pokemon that are given (not caught) are usually excluded from this rule.
- You need to nickname all Pokemon you caught.
- There are also optional rules that you could apply:
  - Either healing Items or the Pokemon Center cannot be used.
  - Disallowing the usage of Pokemon obtained through Trading, NPC, or Distribution Events.
  - No fleeing from wild Pokemon battles.
  - Banning the use of the Master Ball.
There's also a variant of the above Nuzlocke, called the Wedlocke. All of the basic Nuzlocke rules apply, but with an added tint: You must make pairs out of the Pokemon you obtained; when a Pokemon battles, it could only switch out to its partner, and the box could only be used when you're depositing a "dead" Pokemon.
Another variant (called the Wonderlocke) was made possible due to the Wonder Trade feature added since X/Y. It's basically a nasty combination of Nuzlocke and Scramble, in which your caught Pokemon must be sent away with the Wonder Trade, which trades for a random Pokemon. Alternatively, you could also switch your "dead" Pokemon for a random Pokemon with the feature.
Another challenge would be the Bonus Bosses using only level one Pokémon. Bonus points if you manage to do it without giving it the Focus Sash, or without using a Pokemon with Sturdy as its Ability.
Related to the above, there's also the "Youngster Joey" challenge. As its title implies, you can only use Rattata (or its regional variants such as Patrat) in your party.
There's also the generic challenge of using only PokeBall to capture Pokemon, unless forced by the game (e.g. Safari Zone), which increases the difficulty by quite a lot in games where you're required to own the Legendary Pokemon to proceed.
There's also a very minor challenge of not using the game's local Olympus Mons, so you could at least be on similar levels as most NPCs. Be careful though, as certain games have NPCs that use them during the campaign, and the post-game usually have battle facilities with Trainers that use them on the latter stages.
This is mostly for the completionists, but there's also the well-known "Living Dex" challenge, where you have to register and own every single Pokemon specimen available, arranged in your PC boxes in accordance to their National Dex number. Some people also take it further by adding their Shiny variants into the list, which may take literally thousands of soft-resets for guaranteed encounters and extreme luck for randoms. "Gotta Catch 'Em All!", indeed...
Tired of building and raising your team the regular way? Try the "N Challenge", in which you play in a manner inspired by N Harmonia. The core rules are as follows:
- Designate a checkpoint of sorts (the most common ones are "After Gym Battles" and "After Rival Battles"); when you reach a checkpoint, you have to release/box your current team.
- You can only catch Pokemon in areas accessible between the previous checkpoint and the current one.
- You could use your previous team to catch new Pokemon to build your current team, but only for that purpose; you can't use them to progress the game anymore.
- Do not nickname your Pokemon.
- Optional rules include:
  - You may keep your Starter and/or Pokemon given to you by NPCs.
  - You may keep 1 of your previous team's Pokemon after the 5th Gym.
  - You may not have a HM Slave.
  - If possible, your team against the Elite Four and Champion must include the game's box legendary as a member.
Implications and stereotypings aside, there's also the Christian Playthrough and the Atheist Playthrough, which is usually played for some good laughs:
- The Christian Playthrough usually includes the following rules:
  - You shall not evolve your Pokemon.
  - You shall not use the sinister Dark, Psychic or Ghost-Type Pokemon, nor use moves of those types.
  - To breed, your Pokemon must be at Level 22 or higher.
  - Two Pokemon with the same gender cannot share the Daycare Center.
  - It's your duty to keep any Egg you received and raise the Pokemon hatched from it until it reaches Level 18.
  - Do not use fossil Pokemon. Additionally, ignore science labs whenever possible.
  - Do not use the serpents (such as the Ekans line, Snivy line, Seviper, or Dragon-Types); you're also advised to disregard their advice.
  - Legendaries are false idols, and should be exterminated!
  - Do not spend your time at the Game Corners or similar places.
  - Avoid the benefits of narcotics such as PP Up, Ether, or Rare Candy.
- The Atheist Playthrough usually includes the following rules:
  - Do not use the Abra lines, Baltoy lines, Golett lines, Gothita lines, Sigilyph, or the Unowns, as magic do no exist.
  - Do not use the Ghost, Dragon or Fairy-Types, as there's no scientific proof of their existence. Kingdra, Rotom, and the Frillish line are excluded from this rule.
  - No legendaries can be used except Mew, Mewtwo, and Genesect, as you do not believe in those feeble gods. If you count the Ultra Beasts as legendaries, those specimens are also excluded from this rule due to their high scientific value.
  - Revive all fossil Pokemon you can get and keep at least one of those primordial wonders inside your party at all times.
  - Do not cancel a Pokemon's evolution. Let nature take its course.
  - Catch any wild Pokemon you encounter that you haven't got already, FOR SCIENCE! If you're otherwise unable to catch that Pokemon due to reasons such as running out of ball stock, you cannot catch any more Pokemon until that one specimen is yours.
  - Exploiting glitches is highly encouraged, especially glitch Pokemon, since they must be studied.
  - If you have a friend doing the Christian run, battle them before fighting each Gym to prove whose current standing is better.
Some people have also started creating softwares, hacks or custom ROMs for challenges modes, such as ROMs specifically modified with Nuzlocke settings enabled, or the highly popular "Randomized" challenge, where all of the Pokémon encounters (including starters) are entirely randomized.

The Spin-Offs[]

For Pokemon Mystery Dungeon afficionados, there are the challenges involving Kecleon. Some of them include:
- Recruiting Kecleon. This is very hard to do due to the Pokemon's recruitment rate of the abysmal 0,1% chance.
- Stealing from Kecleon. If you're crafty enough to do it, of course. Just be careful of the hordes of Kecleon and the penalty of getting knocked out involving losing all your Items and got them replaced with the Plain Seeds.
- Defeating Kecleon after you stole something from them.