Dimensional Traveler

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A Dimensional Traveler is any character who can (more or less) freely travel between various planes of existence, like parallel universes, etc. Their ability to travel is usually powered by some form magic, Applied Phlebotinum or Teleporters and Transporters (like a Portal Network), but it can also happen that a character was inherently born with such power.

This is also a common explaination for Crossovers, as occasionally the characters will arrive in the universe of another hero.

Distinct from Time Travel because, although Time is considered the "fourth dimension", time travellers otherwise remain in the same plane while hopping between its different time periods.

Fan Works

It happens a lot in Super Milestone Wars and its sequel, Super Milestone Wars 2.
Michikyuu Kanae from Kyon: Big Damn Hero, although she's not doing it for fun, but to survive.
- Also Wataru, Kuyou and a different, Evil Twin Kanae, who have been chasing her since long ago.
The protagonist of Sleeping with the Girls, although he doesn't do it voluntarily. Every time he goes to sleep, he slips into another dimension (and into the bed of another girl, usually with a Tsundere personality).
Delilah from The Legend of Spyro: A New Dawn is a Kitsune capable of traveling through dimensions. This apparently a species trait of her specific type of Kitsune, as it's the only way to leave the Spirit World. After 200 years of traveling the multiverse, she's a Genre Savvy Cloudcuckoolander whose Seen It All. She often drops Shout-Outs to other series which she's visited, most commonly My Little Pony: Friendship Is Magic because she really likes that universe and is best friends with Pinkie Pie. She also mentions the "Cupcakes Incident" frequently, which involved a nasty encounter with Cupcakes!Pinkie Pie and resulted in her being deathly afraid of cupcakes.
This was, for a while, quite a popular device to use to implement a crossover in stories that came out of the now-defunct Anime Fan Fic Mailing List (aka the FFML) in the 1990s, and in fact became the lynchpin around which several epic Mega Crossover fanfic cycles revolve:
- Twister from Twisted Path is probably the Ur Example for fanfiction -- accidentally summoned from his home universe, accidentally empowered to godlike levels by the demon lord whose summoning caught him up, and eventually learning how to transport himself from universe to universe.
- Legion of Legion's Quest was ejected from his home universe by a Freak Lab Accident, getting "smeared" across all his dimensional counterparts in the multiverse in the process, and embarks on a quest to get home using a dimension-hopping starship given to him by his by his future self.
- Shadowrun Wolf shaman Fenris is flung into the world of Bubblegum Crisis by a magical backfire in A Wolf in Crisis by Barry Cadwgan.
- Paramilitary metahuman Col. Douglas Sangnoir of Drunkard's Walk was ejected from his home timeline by enemy action, and is trying to return home by firing himself into the multiverse at random with his powers.
The Dark Kingdom Renegades from the Sailor Moon Expanded project eventually discover how to visit other universes and do so regularly, half as exploration and half as tourism.
The Family from the Worm/Luna Varga crossover fic Taylor Varga eventually figure out how to first view and later visit other universes. As of 2023, their travels are found exclusively in Omake separate from the main storyline, but it's established that most of them are canon to the fic, and show adventures that take place well after the current material. These adventures include such things as restoring the Goblet of Fire to its proper role as a furnace burner for Hogwarts, hunting a magical monster loose in Ankh-Morpork, hanging out with the Avengers, annoying Batman, rescuing a version of Apollo 13 and giving its earth a "Rosetta stone" of math and science, visiting parallel versions of Brockton Bay and doing Speed Runs of fixing all their problems, and... going to SF/Fantasy conventions.

Film

In Indiana Jones and the Kingdom of the Crystal Skull, the Aliens were actually travelers between the worlds.
The Phineas and Ferb made-for-TV film "Phineas and Ferb across the 2nd Dimension" is all about this.

Literature

Robert A. Heinlein's Glory Road. Anyone who understands the metaphysical geometry involved can pass through the Gates and explore the Twenty Universes, and many do so on a regular basis.
- Also in another of his stories, The Number of the Beast. The protagonists use a dimension-hopping device to explore a series of very odd dimensions, including some based on Earth literature.
Keith Laumer's Lafayette O'Leary novels. The protagonist has the ability to travel to feudal/magical alternate Earths.
In the Myth Adventures series, the term "Demon" is short for this.
Philip Jose Farmer's World of Tiers series. Paul Janus Finnegan (AKA Kikaha the Trickster) and Robert Wolff spend much of the novels traveling through artificially created universes.

Live-Action TV

Kamen Rider Decade has this as a major plot point. The previous seasons are revealed as parallel worlds that are merging into one, thus leading everyone of them to destruction, so it's up to the titular hero to journey to each one and destroy them. He even arrived in the World Of Shinkenger on one occasion. The reason being Decade normally travels to RIDER Worlds, and there aren't any Kamen Riders normally in that world until Diend went there, implying there's even more universes than just the Rider Worlds, but only the Rider Worlds are at risk.
Sliders is a series based on this trope, although in the beginning the characters were travelling uncontrollably.

Tabletop Games

Dungeons & Dragons: Anyone with the Cubic Gate or Amulet of the Planes has the ability to be one.
- The people that are seen on the Planescape setting. Many Planar characters use portals on a regular basis to travel between Sigil and the Outer Planes.
Magic: The Gathering. A mage is a planeswalker, able to travel to other planes of existence. The card battles between players represent encounters between planeswalker mages.
In the Yu-Gi-Oh! card game, this is the premise of the D. D. (Different Dimension) cards. Also, while not part of the D. D. set, Neo the Magic Swordsman is described as a dimensional drifter on his card.

Video Games

Tessa from Red Earth is a sorcerologist (one who employs magic in everyday studies to discern the properties of the universe; she's more or less a witch, though). Her knowledge on a wide variety of subject matter in both her home series and various crossovers imply that she frequently treks across the multiverse to broaden her horizons and learn as much as she possibly can.
In Darkstalkers, the only thing linking the Human World and Makai (the Demon World) is a portal located roughly in the middle of Makai, known as The Gate. Morrigan is a special case, in that she can freely travel between the realms independently of this gateway. Being a fun-loving succubus, you should be able to understand why she enjoys this unique ability of hers.
This is the reason why Gilgamesh in Final Fantasy is heavily implied to be the only recurring character in the series to be the same exact character in most, if not all appearances. After being thrown into the Interdimensional Rift by his boss Exdeath for his repeated losses against the party and sacrificing himself to defeat Necrophobe, Gilgamesh simply walks the multiverse via the Void and the worlds connected to it. This is even how he stumbles into the conflict of the gods in Dissidia 012: Final Fantasy; when defeated, a portal leading to the Rift/Void engulfs him, as Gilgamesh, while subject to the war's rules, has no original world to return to.
The Elder Scrolls III: Morrowind: Divayth Fyr is said to be one. According to the in game book The Doors of Oblivion, Fyr is one of the few "mortals" who can freely travel between the realms of the Daedra.

Western Animation

The Road to the Multiverse Episode of Family Guy has Brian and Stewie being one.
In the Transformers Multiverse, many of the "multiversal singularities" are mentioned as having this ability—particularly |The Fallen, Vector Prime, Unicron, and Nexus Prime, as well as the non-singularity Sideways. There's also city of Axiom Nexus, which is roughly analogous to Planescape‍'‍s Sigil mentioned above, and where the inhabitants all have travelling between dimensions down to a literal science.