For fan-fictional to non-canon characters, see here.
Tecton (Mighty Med) connection with the center of the earth allows him to generate strong earthquakes with a stomp when he wants to, but when his body is exposed to Gargulon Gas or at risk he loses control of this power.
Earthmover (Batman Beyond) was buried alive in a toxic waste dump and gained the ability to cause earthquakes and make golems while his body was stuck embedded in a wall for years.
Nico di Angelo (Percy Jackson and the Olympians/The Heroes of Olympus)
Fourarms (Ben 10) using his massive strength to shake the earth.
Armodrillo (Ben 10)
Ultimate Kevin (Ben 10: Ultimate Alien) possesses Armodrillo and Ultimate Aggregor's terrakinesis.
Shock Rock (Ben 10: Reboot)
Earthbenders (Avatar: The Last Airbender) can "bend" (control and manipulate) the earth and ground itself to cause earthquakes.
Goddess of Earth (Charmed) causes an earthquake when she gets angry...
...and opened a chasm in the Earth in the conservatory that swallowed the Titans.
Accelerator (A Certain Magical Index) manipulating vectors to generate a powerful shock wave on the earth.
Arale Norimaki (Dr. Slump) uses the Earth Splitter, a punch to the ground that causes such destructive shock waves that the Earth itself splits open.
Emmet Brickowski (The LEGO Movie 2: The Second Part) using Earthquake Punch.
Experiment 513 "Richer" (Lilo & Stitch)
Dominikos Petrakis/Avalanche (Marvel Comics)...
...Has earth powers.
Juggernaut (Marvel Comics)
Julio Richter/Rictor (Marvel Comics)
Crystal (Marvel Comics)
Quake Woman/Tempo's (Mega Man Archie Comics) Quake Drill was primarily made for burrowing, but can cause earthquakes which she earned her name for
Ground Pound Magisword (Mighty Magiswords) can generate earthquakes by slamming onto the ground.
Lord Tirek (My Little Pony: Friendship is Magic) using his strength to smash the ground beneath him.
A Tremor Human, Edward Newgate/Whitebeard (One Piece) could use his shock waves to cause massive earthquakes thanks to his Gura Gura no Mi powers.
Marshall D. Teach/Blackbeard (One Piece)
Saitama's (One-Punch Man) virtually unlimited strength can create massive shockwaves and craters in planet-sized objects with ease.
Slaking (Pokemon) vibrating the ground causing an earthquake.
Tauros (Pokemon) using a move known as Fissure.
Jesse Turner (Supernatural) causing minor earthquakes when angry.
As the Guardian of Earth, Cornelia Hale (W.I.T.C.H) has the elemental ability to create massively strong and powerful earthquakes.
Stonedozer (Power Rangers Ninja Steel)
Hard Man (Mega Man 3)
Concrete Man (Mega Man 9)
Naturon Shenron (Dragon Ball GT)
Dark Danny (Danny Phantom) was able to use his Ghostly Wail to cause a powerful earthquake inside the artificial Ghost Shield, a feat none of his other powers could do then.
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