A rich and varied multiverse like the one Magic takes place in is bound to be full of many different species. Some of them are familiar to us from our own world and from other fantasy stories; others are so utterly different from the creatures found in other tales that we can confidently say we'd only encounter one on a plane in Dominia. A surprising number of the creature types in Magic were created from scratch - here are my five favorite examples.
Kor (Devout Lightcaster)
The Kor got their start as one of the three holy wasteland tribes of Rath in Tempest block - along with the Vec and Dal, they anticipated the coming of a messianic figure appropriately called the Korvecdal who would help them overthrow Volrath's tyranny. But although the Vec and Dal were human, the Kor were something else entirely - pale, lithe, and catlike, often with a bluish tinge to their complexions. Since this was before the era of race and class types, the Kor didn't get their own creature type until they resurfaced in Time Spiral block, and then again in Zendikar block in which it was revealed that they adapted so well to Rath because the harsh world of Zendikar was their home plane.
Ah, Thrulls - the classic case of why you shouldn't mistreat your servants. The misshapen pseudosentient freaks that were the original Thrulls, in Fallen Empires, were created with profane alchemical processes by an Ebon Hand priest named Endrek Sahr, Master Breeder. He made them to be able to take an obscene amount of punishment and repurpose their own dead flesh, which worked all too well once the Ebon Hand cruelly overworked their new servitors and were promptly greeted with a slave rebellion. The Phyrexians took a shine to Thrull-making and brought them to Rath, but it wasn't until Ravnica block, when the Orzhov made ostentatious, self-righteous, and actually obedient Thrulls, that they really made a comeback.
Moonfolk (Meloku, the Clouded Mirror)
The time between Invasion and Time Spiral blocks was a troubled era for blue's small creatures. See, around the time of Odyssey block, Creative decided that Merfolk were a bad fit for a game presumably themed around mage duels based on land. So each block we were treated to a new attempt at revamping the blue weenie - Odyssey's seaborne but still amphibious Cephalids, Onslaught's more traditional Illusions and Wizards, Mirrodin's serum-twisted Vedalken, and then the lop-eared fops of Kamigawa, the Moonfolk. None of these really stuck, although Vedalken keep coming back for various reasons, but the Moonfolk were really memorable for reasons other than the oppressive decks they enabled - a reference to East Asian stories about a rabbit in the moon, they were truly Magic's version of pompous, overly-learned feudal Japanese courtiers.
The thing that menaced Saffi Eriksdotter and her hapless brother Hans is... well... it's kind of... really more of a... okay, physical descriptions are hard when you don't know where to start. Crocodile, leech, and wendigo jump to mind at first glance. Anyway, the original corpse-eating strain eventually branched off into many, many subspecies of Lhurgoyf that excelled in feeding on anything used-up, including one infamously powerful strain that eats variety itself.
Ol' Resident Teeth here made my oddest creature types list as well, so you know it has to be doing something right. From humble beginnings as a one-off card with humorous flavor in Antiquities, Atogs have become a recognizable symbol of, well, Magic itself. And there are tomes and tomes to be written about their digestive systems alone.