From Bulbapedia, the community-driven Pokémon encyclopedia.
The Pokémon world is not the only place in its universe that Pokémon exist. There exist several Pokémon that originated somewhere through space and have migrated there, as well as those who reside in their own dimensions. Many of these Pokémon can breed with terrestrial Pokémon, and evolve in the same ways. Poké Balls and items that work on terrestrial Pokémon work just as well on these. These Pokémon have apparently adapted to the place where they landed on Earth.
There are also myths involving Pokémon originating outside of the Pokémon world because of their resemblance and relation to extraterrestrial bodies, and in some canons there are characters who speculate non-earthly origins for all Pokémon.
Some Pokémon have been confirmed to originate in places other than the Pokémon world.
Only one Pokémon is known to come from outer space. However, whether Deoxys was, strictly speaking, an actual Pokémon prior to its arrival differs by canon.
Deoxys came to earth in a meteor.
A space virus fell to earth in a meteor, and was exposed to a laser beam. This caused the virus's DNA to mutate into the Pokémon Deoxys. Upon exposure to a meteorite, Deoxys's Forme will change. Deoxys has four formes, adapted for survivability in the wild, and its specialized formes have some of the highest base stats of any Pokémon. Its Attack Forme is adapted for combat against Pokémon native to earth, its Defense Forme is useful to protect itself from attack from Pokémon native to earth, and its Speed Forme is useful for fleeing. These formes in combination with its ability to regenerate lost body parts allow it to survive in an alien world. Because of its exoticism, it is generally asocial. Deoxys is not a unique phenomenon, and a Deoxys can communicate with others of its kind by creating an aurora.
Several Pokémon are known to exist or originate in alternate dimensions, either in the sense of parallel universes, or in the sense of additional aspects of the main universe unobserved by humans.
Unown in their alternate dimension
Unown originate from an alternate dimension. People, such as Spencer Hale in Spell of the Unown, have been known to be transported to their dimension and Unown have been known to come from their alternate dimension into other dimensions, such as an Unown in Address Unown!. Several Unown also are found in the Ruins of Alph, Tanoby Chambers and Solaceon Ruins but it is unknown how they came to be here, whether they came here from another dimension or originated here.
The Time Travel Pokemon can travel through time, which is a dimension.
#480 Uxie, #481 Mesprit & #482 Azelf
The anime shows that the members of the Lake Trio reside in pocket dimensions whose entrances are within their respective lakes.
Dialga lives in its own dimension, from which it governs temporal matters. This dimension collided with those of Palkia and the Unown in The Rise of Darkrai, and, each thinking that the other was trespassing, Sinnoh’s legendary Pokémon began to clash. In Pokémon Diamond and Platinum, Cyrus summons Dialga from its dimension to the Spear Pillar using the Red Chain. In Platinum, a portal to Dialga's dimension appears at the Spear Pillar if the player has the Adamant Orb. Notably, this portal will never appear at the same time as the portal to Palkia's dimension.
Palkia lives in its own dimension, from which it governs spatial matters. This dimension collided with those of Dialga and the Unown in The Rise of Darkrai, and, each thinking that the other was trespassing, Sinnoh’s legendary Pokémon began to clash. In Pearl and Platinum, Cyrus summons Palkia from its dimension to the Spear Pillar using the Red Chain. In Platinum, a portal to Palkia's dimension appears at the Spear Pillar if the player has the Lustrous Orb. Notably, this portal will never appear at the same time as the portal to Dialga's dimension.
Giratina lives in a parallel dimension of antimatter. In the anime, this dimension is the Reverse World; in the games, it is the Distortion World. In both dimensions, the normal rules of time and space do not apply. When it is not in this dimension, Giratina assumes its Altered Forme, however, holding the Griseous Orb reverts it to its Origin Forme. Because the other dimensions are inextricably linked with Giratina's dimension, Giratina will viciously defend its world if events in other dimensions threaten it.
Arceus lives in a high dimension, from which it stands guard over the entire Pokémon world, and will wake from its slumber to save it from annihilation. In the games, this dimension is the Hall of Origin. The only way to get there is by blowing on the Azure Flute, which has not been legitimately released, at the Spear Pillar, the highest point in Sinnoh.
Darkrai resembles a shadow, has power over dreams, and can hold it's own with extra-dimensional monsters. It's shown in M11 that there exists a dream dimension. Quite possibly this nightmare Pokemon is from there.
Cresselia has power over dreams, in universe where a dream dimension exists, and like other psychic types, it has an outer-space theme to it. Quite possibly this dreamy Pokemon is from the dream dimension.
#173 Cleffa, #035 Clefairy, and #036 Clefable
The star-shaped Cleffa are said to have come to earth on meteorites. Wherever a meteorite lands, there is always a Cleffa near. Cleffa and their evolved forms, Clefairy and Clefable, dance in a ring on Monday nights, nights with a full moon, and on nights when meteor showers occur. Clefairy and its evolutionary relatives tend to make their habitat at impact sites, and Clefairy evolves into Clefable from a Moon Stone, further evidence that they are extraterrestrial in origin.
In the anime, Clefairy have been shown to be capable of constructing aircraft and runways, which could offer another explanation for their origins.
The manga chapter Clefairy in Space from The Electric Tale of Pikachu revolves around the idea that Clefairy are extraterrestrials.
#120 Staryu and #121 Starmie
Starmie are said to be extraterrestrials because they are star-shaped and they emit radio signals into space at night. Staryu gather at night and flash their red cores to communicate with the stars.
#337 Lunatone and #338 Solrock
Lunatone and Solrock are said to have come from space and to be from the moon and sun, respectively, from which they gain power. They are both known as "Meteorite Pokémon," as they were discovered near meteorites. In the anime, Tate and Liza stated that their Lunatone and Solrock were brought back by their astronaut father from a mission on the moon.
In the anime, Jirachi descended from outer space in the Millennium Comet, which is visible from the Pokémon world for only seven nights once every thousand years. The origin of this comet, or Jirachi itself, is unknown, and as such, it is not known if there are any other Jirachi left in existence. It is also based on the concept of wishing upon a star.
#605 Elgyem and #606 Beheeyem
Elgyem and Beheeyem allegedly appeared 50 years prior to the events of Black and White Versions in the Desert Resort. It is unknown how or why they appeared. This could be explained by their ability to rewrite the memories of the people and Pokémon around them. They survive hostile encounters by using their psychic powers to confuse opponents. In the present day, they are no longer found in the desert, and have relocated to high up in the Celestial Tower and Unova Route 14, respectively. In Black and White Versions 2, Beheeyem are no longer found in Unova Route 14. These Pokémon appear to be based on alien conspiracy theories including those surrounding Area 51 and the Roswell incident.
In an old legend in Lacunosa Town, a large meteor fell from the sky, apparently containing Kyurem. At night, the "monster" would bring cold winds and take people and Pokémon away, to eat them. The town residents then surrounded Lacunosa Town with a wall to keep Kyurem out, and a rule was set on the town that forbade anyone from leaving the town at night, and encouraged them to stay in their homes. Even to this day, the residents remain in their houses at night and the wall is still standing. Kyurem lives in the Giant Chasm, the impact crater of the meteor which supposedly brought Kyurem to Unova. However, in Black and White Versions 2, Kyurem is stated to have been part of the Original Dragon that split into Reshiram and Zekrom. As this event occurred on Earth, this conflicts with events that happened as stated in the legend.
#174 Igglybuff, #039 Jigglypuff, and #040 Wigglytuff
Jigglypuff gave signals on Oswald's device in Clefairy Tales. Additionally, the fact that Jigglypuff is commonly found living near impact sites, and that it evolves from a Moon Stone, could be seen as evidence that Jigglypuff and its evolutionary relatives, Igglybuff and Wigglytuff, are extraterrestrial in origin.
Mew is said to be the ancestor of all Pokémon. Due to this, and the number of extraterrestrial Pokémon that have been discovered, it is possible that Mew inhabit other areas of the universe, and it is equally possible that they originate from a world other than Earth. Mew have been shown to be capable of flying through the vacuum of space, as displayed in the original Pokémon Theme.
Misty's Togepi made Oswald's device ring when it was pointed at it. This could be evidence that Togepi is from space.