User-created contests are unoffical games you can play that were not intentionally added to the game. These are not offical, but are worth mentioning. This list is not finish and it's unlikely it ever will be.
Pokemon Contests can have roleplay elements mixed in, but only on rare occasions. The first round is a comparison between the Pokemon, based on the judge's opinion and the Pokemon who suits the theme better. Shiny Pokemon may have a point boost or drop. The second round is appealing, where the users' pokemon must defeat 1 wild pokemon in that area using only one move. This same move can be repeated. WHoever defeated the Pokemon quicker wins that round. At the end, there is a final result for who got more points overall.
Pokemon Wrestling sounds like an odd idea at first, but it's logical at the Construction Site where the 3 compatible pokemon can push crates around and force opponents off the top. (The compatible Pokemon are: Aggron, Golem, and Rhydon) The goal is to go to the top of the construction site, battle your enemy with one of the compatible pokemon. The objective is to push the other pokemon off the field. Regardless of who faints first, the first to fall off loses. If both are on top, and one faints, the fainted pokemon loses.