These are challenges I've done:
Contests challenge: A pokemon's moves must be all the same contest type: smart, beauty, etc. For my treecko I stuck with smart. worked out for me :D
Moveset challenge: As your pokemon learns new moves, the newest move will replace the oldest move, no matter what moves they are. TM's are not allowed. HM's, when taught, will still replace the oldest move when taught. This is honestly the hardest challenge I've done.
Split-game Challenge: Using any games that come in threes(Ruby, Sapphire, Emerald; Diamond, Pearl, Platinum; and so on) play all 3 at once. However, once a pokemon is caught in one game, it cannot be used in the others. For example: you catch a poochyena in Emerald. You can't use a poochyena or it's evolution in Sapphire or Ruby. The games should be kept at about the same place in the story at once. It took me forever to beat this challenge.
Restriction Challenge: Starters are excluded from the following: Roll a dice and see what it lands on. Anything from 2-6. Let's say it lands on 3. Then, every third pokemon in the pokedex, including it's evolution, if it evolves, can't be used in game. The pre-evolutions are allowed, but not that pokemon, or what it evolves into. Use the region dex, or the national dex, depends on how challenging you want it to be. I used region on Diamond, and I rolled a two. I was tempted to roll again.
Random Favorite Challenge: (This challenge will most likely involve Action Replay usage) Make a list of your top 6 pokemon in every type. Make sure you have them arranged from favorite to least favorite. Then, get someone to pick 6 random types. Let's say they pick: Dark, Grass, Fire, Electric, Ground, Bug. Then, you have to arrange a team depending on what they chose. Since dark was first, use you favorite dark type. Then, since it was second, your second favorite grass, and so on. When I did this, I ended up with 5/6 being weak to electric. Though, it can be pretty fun. This is the one I do every time a new generation is made.
I made all of these myself. If there are ones similiar like them out there, I never saw them.
I
really like the split game, moveset, and favorite challenge. One question for moveset-would you be able to choose not to learn a move? It would suck if you had a Charizard or something that didn't have any fire moves because there was like 5 moves in between ember and flamethrower (don't know if that's the case, just an example).
I agree with Sydian concerning those challenges - I like all of their ideas. =D However, I do have three on my hands right now (baaaaad idea, kids) so I think I'll just need to save their concepts on a Word document and do them later, after I've finished the giant pile of game-playing before me. xD
And I would put a Legendary cap on the favorites challenge, like two Legends for the entire group. They can be used in any of the types, but you only get two. For example, if you like Heatran and Rayquaza, you would have one in Steel and one in Flying (or one in Fire and one in Dragon). I can point to quite a few Legendaries that I like very much - including, amazingly, Giratina - but I can see how it would be a game-breaker. Though you would probably have to put up your list first and leave it to the creator of the board (or a team the creator trusts) to pick them for you, akin to the Random Pokémon Challenge or something.
Anyway, I was thinking of a one-time challenge where you are only allowed to use Pokémon given to you from NPCs exactly as they are - meaning you can't evolve them. For example, a Starter Pokémon given from a Professor, the Onix you get for a Bellsprout in G/S/C/HG/SS, or the Eevee you find in the big building in Celadon or something. It wouldn't be the most gut-wrenchingly difficult of challenges, but I can't think of many people who would normally construct a team of Abra, Chatot, Haunter, and Magikarp.
Pssssssssh only doing 3 challenges at once. Puh-leez. If I'm doing any less than 5 at once I think its a light load.
I think the rule should be that you can add legendaries to your team, but you would only be allowed one. So, if you really like Zapdos and Mewtwo, you would have 7 Pokemon in both the Psychic category and the Electric/Flying category (whichever you put Zapdos in). That way, if Mewtwo is chosen first, then you ignore Zapdos in his list, and the 7th Pokemon either takes his place, or all the Pokemon after Zapdos move up a position.
I think the third paragraph was idea-ized before, but got vetoed because there aren't many Pokemon you could choose from.