Ogres are massive, brutish humanoids with low intelligence (with some exceptions) and great bloodlust. They appear in many different planes in many different forms, and are primarily associated with red and black. The first ogre ever printed in Magic was Gray Ogre, which was the only creature of the type in Alpha.
Ogres can be found on many places on Dominaria, among them Keld, Otaria and Caliman. Those who live on Caliman, like many of that island's denizens, have access to more advanced technology, such as mechanical sawblades powered by Phyrexian mana batteries.
Known as o-bakemono, the ogres of Kamigawa are more intelligent than ogres of other worlds and possess considerable brute cunning.   They originated in the Sokenzan Mountains, though most of their kind later removed to the swamps of Takenuma. Most of these ogres cared for little but to inflict pain, murder innocents, and worship the demonic oni, though some ogres rejected the oni and remained in the mountains were cursed and made outcast by their brethren; some of these joined forces with the ronin of the mountains and became samurai themselves. 
The o-bakemono were in the thrall of the oni and worshiped them with foul blood rites and sacrifices of living sentients in exchange for gifts of strength and supernatural powers.  With the advent of the Kami War, the o-bakemono succeeded in freeing many of their oni masters from their spiritual prisons, together hoping to destroy Kamigawa. The most fearsome stronghold of the demon-worshiping o-bakemono was the blood-stained keep of Shinka, where dwelt the dreaded ogre shaman Hidetsugu.
The Mirrodin Ogre is too dense to recognize a threat of any sort, consuming whatever they feel like, and easily outsmarted by goblins who use them as beast of burden. Mirran ogres are famed for crushing artifacts. 
The Ogres on the city plane can actually be reasoned with, but are nonetheless slow thinkers and easy to deceive. They are featured in all the red guilds (both in cards and the novels): Boros Legion, Izzet League, Gruul Clans, and Cult of Rakdos.
The ancient Ogre civilization of the Onakke upon, Shandalar, were creators of the Chain Veil  The Onakke were utterly obliterated by a magical spell, cast by an unknown source. Their spirits haunt the Chain Veil, and its owner Liliana Vess, while their bodies are in the Onakke Catacomb.
The massive ogres of the Mardu Horde on Tarkir are stronger than orcs, but of feral-level intelligence. They are uncontrollably violent and are kept chained until they're sent at the enemy to stir up chaos and cause destruction.
- Goka the Unjust. An opportunistic shaman on Kamigawa.
- Hidetsugu, the warden of Shinka, the ogre hermitage high in the Sokenzan range of Kamigawa. A powerful mage who serves a great oni.
- Kazuul, Tyrant of the Cliffs of Murasa in Zendikar
- Kuon. An o-bakemono whose blood-magic meditations elevated him into the essence of pain and agony.
- Kurkesh, Onakke Ancient
- Ruric Thar, a twoheaded mazerunner from Ravnica
- Magic Arcana. (February 09, 2005.) "Sketches: Flames of the Blood Hand", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (February 22, 2005.) "Whenever Ogre Marauder Attacks", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (July 12, 2005.) "Renegade from the Mountains", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (July 06, 2005.) "Sketches: Raving Oni-Slave", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Doug Beyer. (February 09, 2011.) "Public Displays of Aggression", Daily MTG, magicthegathering.com, Wizards of the Coast.
- James Wyatt. (July 2, 2014.) "Veil of Deceit", Daily MTG, magicthegathering.com, Wizards of the Coast.