The user can create, shape and manipulate dimensions, beginning with the physical 0-D, 1-D, 2-D, 3-D, and 4-D, changing their own dimensions. Advanced uses include manipulation and linking to alternate dimensions and dimensional energy to achieve a variety of feats, such as teleportation, portal generation, and pocket dimension creation.
There are various types of dimensions and what composes them, such as time, space, reality, nothingness, and universes, so a Dimension Manipulator with little to no restriction can basically manipulate them all. A master can even create a pocket dimension out of nothingness, and completely create a new world.
Georg (Highschool DxD); via Longinus: Dimension Lost
Yuko Ichihara (xxxHolic)
Diane Taylor (Mutant X)
The Boneless (Doctor Who)
Dawn Summers/The Key (Buffy the Vampire Slayer)
Twilight (Buffy the Vampire Slayer)
D'Hoffryn (Buffy the Vampire Slayer)
Willow Rosenberg (Buffy the Vampire Slayer)
Vengeance demons (Buffy the Vampire Slayer)
The First Evil (Buffy the Vampire Slayer: Chaos Bleeds)
Senior Partners (Angel)
Mistress Meerna (Angel)
Tall Man (Charmed)
Blue (Blue's Clues)
Breach (Generator Rex)
Professor Paradox (Ben 10: Alien Force/Ultimate Alien)
Alien X (Ben 10)
All Celestialsapiens (Ben 10)
Pariah Dark (Danny Phantom)
Grim (The Grim Adventures of Billy & Mandy)
Planet Express Ship (Futurama)
Dr. Dimensionpants (Dr. Dimensionpants)
Diagon (Ben 10: Ultimate Alien)
Lion (Steven Universe)
Discord (My Little Pony: Friendship is Magic)
Hekapoo (Star vs. the Forces of Evil)
Jareth, the Goblin King (Labyrinth)
Ramona Flowers (Scott Pilgrim)
Gideon Graves (Scott Pilgrim)
Bulk Beings (Interstellar)
Murtaugh (Submachine series)
Shang Tsung (Mortal Kombat)
Solaris (Sonic the Hedgehog)
Mephiles The Dark (Sonic the Hedgehog)
Time Eater (Sonic the Hedgehog)
Demise (The Legend of Zelda: Skyward Sword)
Dimentio (Super Paper Mario)
Count Bleck (Super Paper Mario)
Tabuu (Super Smash Bros. Brawl)
Evil Twins (Crash Twinsanity)
Xehanort (Kingdom Hearts)
Xenmas (Kingdom Hearts)
Ansem imposter (Kingdom Hearts)
Chakravartin (Asura's Wrath)
Muzét (Tales of Xillia)
Demise (Valkyrie Crusade)
Erazor Djinn/Alf Layla wa-Layla (Sonic and the Secret Rings)
Daedra Princes (The Elder Scrolls)
Shade-Master (Master Defenders series)
Fanoxean (The Young Guardians)
SCP-507 (SCP Foundation); involuntary
Lee (Channel Awesome: Two-Year Anniversary special Kickassia)
All members of the royal family of Amber and their descendants (Chronicles of Amber)
People from Chaos (Chronicles of Amber); while near the courts of Chaos.
Wizards from Chaos (Chronicles of Amber)
Some demons (Chronicles of Amber)
Mystery Wall (The Simpsons)
Doctor has absolute control over his own Warp World dimension, a realm he created with his chi.
Shinobu Negero (Buso Renkin) using his Secret Trail to cut open a pathway to another dimension that only his DNA can enter, and hide within.
Road can create her Dream pocket dimension, and then manipulate it to her liking.
Super Boo unleashes a mighty scream that tears a hole in the very fabric of dimensions, and is potent enough to destroy the entire universe if he goes too far.
Janemba (Dragon Ball Z) can manipulate dimensions to open portals that redirects his fists closer to his opponents, as well as remove the barriers between Earth and the Other World and allow the dead to reenter the world of living.
In his final form, Janemba's dimensional manipulation abilities increases to the point he can teleport parts of himself and send slices through the dimensional barriers.
Obito (Naruto) can distort the fabrics of space-time to absorb his opponents into the space-time dimension within his Kamui, and can manipulate the insides to keep them trapped and even under illusions.
Kaguya Ōtsutsuki (Naruto) has absolute control over her own personal dimension, capable of shifting herself an people around her into it, and rewriting the environment within to her likings.
Giratina (Pokemon) can control the dimensional energy by opening portals between this world and Distortion World.
In the Distortion World, the dimension Giratina originates from, it has absolute control over it.
Giratina can dive into its own shadow, which is a portal to the other dimension, and move about undetected.
Akua can shift herself from the dimension in which she exists, so she can become intangible for both near unstoppable offense and invulnerable defense.
Akua can apply the dimension-warping power of the Dimension Blade for her entire body, allowing defensive intangibility and phasing through walls.
Despite the name, Makora's Shadow Techniques are actually manipulating dimensional energy to create pockets of black empty space for a variety of feats.
Makora using Kage Hoyo to travel between the dimensional space he created, which also effectively hides his ki.
Makora using Kage Ochi that drags the victim into the shadow dimension for eternity, with nothing but darkness until death.
Makora using Kagegromo Kjokueiki to wrap himself in dimensional energy to form an armor of shadows.
The Kagegromo Kjokueiki grants the user intangibility as it transfers the incoming attacks to the shadow dimension.
Chaos Control, when used at powerful enough levels, can allow the users to warp and travel between dimensions, stopping time and such.
Solaris (Sonic the Hedgehog) is a super-dimensional lifeform who can manipulate the very dimension of space-time and is an omnipresent god of the sun and time.
Mephiles the Dark (Sonic the Hedgehog)
Time Eater (Sonic the Hedgehog) possesses the power to transport individuals and entire locations into White Space, a blank, timeless dimension.
Ixis Naugus (Archie's Sonic the Hedgehog) is the creator of the Zone of Silence, and is thus omnipotent while he is inside it.
Dimentio (Super Paper Mario) is a self-proclaimed "master of dimensions."
Tabuu (Super Smash Bros. Brawl) can manipulate the entire Subspace dimension, being the very master of it.
Muzét (Tales of Xillia) is a Great Spirit who wields power over dimensions.
Midna (The Legend of Zelda: Twilight Princess) can manipulate the dimension of the Twilight Realm to form portals and move between dimensions.
Zant can manipulate the dimension of the Twilight Realm, changing the very dimension of the battlefield to elsewhere, as well as move between the two realms.
Mistress Meerna (Angel) is an expert in inter-dimensional magic.
Yuko Ichihara (xxxHolic), the Dimension Witch.
Demise (Valkyrie Crusade) can manipulate dimensions, destroying her foes in dimensional rifts.
Alf Layla wa-Layla (Sonic and the Secret Rings) has transformed the entire Arabian Nights dimension into a black void.