I know of the Nuzlocke Challenge, and a lot of people do mono-type games, but what are some other challenges for Pokemon games?
(Someone tell me if this isn't allowed, but I double-checked the rules and this isn't an opinion question nor poll)
i found this there are lots of challenges. This is one of them
More Challenges Here
You go through a game with a team picked by others. The first six people to post Pokemon are the Pokemon you use, each user may choose two Pokemon for the player. You can build the movesets of the Pokemon used in this challenge.
Besides a Solo Run(where you use one and only one Pokemon) there really isnt anything else. You can come up with you own game modes with your own rules, like you can only use Pokemon that are under a certain Stat total.
http://www.neoseeker.com/forums/2969/t859012-pokemon-game-challenge-way-to-make-game-harder-may-contain-spoilers/ (most of page is about yellow red and blue)apart from the ones listed there the wedlocke challenge where if you have a male Pokemon the next one will be a female Pokemon and MUST pair them if one of them faints the other one must take care of the battle and no switching to other pairs if one faints the change the fainted Pokemon with a other female or male cannot deposite them that counts as a faint genderless Pokemon does not count so legendarys (exept heatran, latios, latias and creselia doesnt count) and solo run (wedlocke rules: http://www.smogon.com/forums/showthread.php?t=34769759)