The story of WAAPT spans a rather large multiverse, and while most events take place in one of them, others occasionally come into the spotlight. Here are some that have:
Original Timeline: The universe where most of the RP takes place. Also known as the OU, or Original Universe.
Alternate Timeline or AU: A "darker and edgier" alternate universe split off from the OT by the legendaries due to the actions of Cyrus.
Another Universe: A "lighter and softer" alternate universe with many differences from the OT. Also known as the Other or Another Day Universe.
PMD-A: The universe of the Pokemon Mystery Dungeon games.
PMD-B: A post-apocalyptic branch-off of the AU where humans are virtually extinct.
Netherworld Universe: Not much is known about this universe.
No Moon Universe: A universe where a Poison-type legendary is fighting its way back into canon against a Nidoran.
Diamondverse, Pearlverse, Dawnverse: Universes with alternate versions of DS's initial journey. Diamondverse takes after Pokémon Diamond, Pearlverse Pearl, and the Dawnverse is a universe where Dawn didn't get the cold that allowed DS to take her place in the OU and AU.
Animeverse: The universe in which Red was replaced by Ash Ketchum, possibly as a result of other divergences in its history.
PlatinumTaggverse: A universe where Tagg ended up being the savior of Sinnoh instead of either Dawn or DS.
Phosphoraverse: The universe where Phosphora comes from, which is implied to be a canon future of the OU.
Awakeningverse: A distant universe near-identical to that of RL!Fire Emblem Awakening, from which Robin hails.
Yangverse: A universe that plays by notably different rules than the normal WAAPT timelines yet has certain similarities belying an underlying close connection. Meta-wise the shared setting of most all of the Pokemon fanfics by a certain player.
StarFox!Verse: A universe based on the StarFox series, with the planet Falconan taking elements from F-Zero, inhabited by humanoid mons. Humans and Pokémon from elsewhere who visit will also take on a humanoid mon form.
687th Parallel Universe: Not much is known about this universe (not even whether it's really the 687th) other than that the resident Arceus is very poor.
Giant Sea Creature Universe: A universe overrun by giant aquatic Pokemon.
Evil!Goggles Universe: A universe in which an evil version of Goggles is planning to steal all the sand from all the other worlds in the multiverse in order to make the Route 4 desert in his universe the biggest desert ever.
Stolen World: A universe stolen by Swindle. All that is known about it is that, at some point, Professor Rowan, Saturn, and Cynthia team up to stop an Eldritch Abomination.
Westeros Universe: A universe where the weather patterns are akin to that of Westeros from the series A Game of Thrones.
Alt PMD-B: A version of PMD-B in which within Unova the dragons didn't shut down the power grid, making technology levels comparable to that of the modern AU.
FFV!Verse: A mon based universe based on that of Final Fantasy V.
Mario!Verse: A mon based universe based on the Super Mario Bros series.