Diminutive, often chubby or rotund, pastoral humanoids, halflings don’t appear in a lot of “mainstream” fantasy or urban fantasy. They could be adapted to either, though, or even played with by basing them off a wide variety of “little people” that appear in global folklore.
Tolkien first created the halfling, as Hobbits, possible basing them loosely on the “Little People” of English folklore. They were a tough, pastoral folk excellent at concealment and enjoying “simple” lives. They were very much a sort of representation of Tolkien’s idealized pastoral English middle class.
Halflings mostly appear in RPG related fiction, tabletop games, and video games. They are hobbits under a different name due to copyright issues, but have essentially the same traits as Tolkien’s hobbits. Over the last few decades, some game (D&D, for instance) have introduced different varieties of halfling. One of the most notable variations is the Margaret Weis & Tracy Hickman kender—kleptomaniacal halflings cloaked in an innocent demeanor and hyperactive chatter.
George Lucas and Ron Howard created their own variation for the movie Willow. Their Nelwyns are clearly similar to halflings, though they appear a bit darker, or more realistic, and much more like the Sackville-Bagginses than the idyllic Gamgees in many ways.
Merfolk are partly humanoid fish people that have had a variety of physical appearances. A classic version is a human top and fish bottom, as seen in mermaid tales. Others are entirely aquatic and fish-like in appearance, although with a humanoid top half (as in Sci-Fi’s show Sanctuary). Some herd sea creatures or cultivate sea plants. Most hunt sea animals and almost all use echolocation to some degree. Unfortunately, because of their aquatic nature, they can be difficult to work into human focused stories and worlds, although they do appear in some of the Dragonlance novels and many fantasy RPGs. Merfolk could be potentially active and interesting in a Venice-based fantasy city or urban fantasy story, living in lagoons and canals. They could even potentially work in a city with multiple decent sized rivers or a river delta.
Rowling introduces a settlement of merfolk in the Hogwarts lake, preserved there and safe. These merfolk are friendly to Dumbledore, who speaks mermish. They only appear a few times, though, notably for a Triwizard Tournament event and for Dumbledore’s funeral.
The minotaur originates in Greek myth, where it was a bull-headed humanoid. That element of appearance has been retained, though there is debate about whether minotaurs should have human feet or bull feet. There are a host of other appearance elements and uses in modern fantasy and urban fantasy, but they all generally agree that minotaurs are taller than humans and have bull (or cow) horns. Most varieties have tails.
In the Greek myths, the minotaur was a unique being, a child of the Minoan queen Pasiphae and a bull meant as an offering to Poseidon. It was kept in the Labyrinth where it ate an annual sacrifice of humans. What it did between the Athenian tributes is unclear, but presumably Minos was exacting tribute from other cities as well.
Rick Riordan continues to hold with the classical sources with a unique Minotaur. His Minotaur is an axe or sword wielding beast bent on killing demigods.
The Dragonlance creators took the minotaur myth and spun it into an entire species of beings. Their minotaurs form an honorable warrior culture governed by the winner of arena combat. They are excellent sailors. Unfortunately, they often find themselves beholden to the forces of Takhisis (in the time of Huma and the War of the Lance).
Tonya Huff (The Enchantment Emporium) makes brief mention of minotaur cattle ranchers in central Canada. No other description appears, but presumably the minotaurs are a species of beings and they seem to be relatively inoffensive—as ranchers and there’s no worry that the protagonist’s grandmother appeared to be on good terms with them.
According to classical sources, nymphs are representatives of nature. They are typically described as all being female, sort of counterparts to satyrs & fauns. Many are tied to specific locations and able to exert some degree of control over their natural feature. As legends evolved, nymphs became tied to sexuality as well, which is not necessarily true of the mythic stage. In the early phase of their development, they were more focused on nature and roles as children of lesser gods.
For the Greeks (and Romans), there were many varieties of nymphs from meadows to trees, oaks to rivers, oceanic to the daughters of Atlas. They were always female and were often pursued by satyrs and gods alike.
Rick Riordan remains true to the classical sources, depicting his nymphs as the female counterparts to satyrs. In this form, they have a somewhat symbiotic relationship with the all male satyrs. Many of the nymphs serve and protect Camp Half-Blood, but there are exceptions who are tied to other parts of the world, such as Artemis’s nymphs.
Jaye Wells makes nymphs into a nature oriented sub-species of the Fae race. Only one, Vinca, is shown in detail. She exhibits power over plants, particularly enhancing and accelerating their growth, and hated cats as an ancestral enemy.