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 Pokémon 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, successfully as Eternatus as of the end of the Entralink Arc.
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.
PMD-N: A universe based on the Elder Scrolls series, with a similar transformation effect to PMD-A and B. Short for PMD-Nirn.
No Sun Universe: A universe where the sun disappeared at some point in 2016. Investigation into how or why is ongoing, but Necrozma is suspected.
PMD-S: A PMD-verse based on the Shining series. Short for Shining Force, also known as PMD-R, or Rune.
Pokefuturesverse: A universe where the PEFE Founders failed to stop Pokefutures, and in their search for mons for Drives ended up extincting virtually all the mon population and poisoning the planet, necessitating the stealing of mons from other universes. Currently turned into a mostly mon-only verse like PMD-A and B.
TPAAWverse: A universe turned completely chaotic by Glitch energies that serves to protect other nearby universes from meeting the same fate by serving as a Glitch sponge that siphons the majority of it away from everything else.
Ironverse: A universe where Team Iron managed to succeed in its goal of killing off the legendaries, but started an apocalypse.
Fledglingsverse: A PMD-universe based on the one that appears in the Pokémon Mystery Dungeon fanfic Fledglings by Tracer Bullet, though altered due to Hess' band of pirates ending up in OU!Alola due to the multiversal wall breakage taking place during the Entralink Arc.
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.
Travel Between Universes
Most people travel to other universes using the Entralink, but other methods include the use of a Griseous Orb, direct help of legendaries capable of interdimensional travel, Ultra Wormholes, or man (or mon)-made technology.