There's a wide variety of species that have come to inhabit the Wastelands, both sentient and not. This post will provide a brief overview of some of the key races. Many of them are heavily inspired by those as portrayed in Shadowrun; very few sentient races are automatically evil as they might be in a system such as D&D.
Humans: Humans, having developed as inhabitants of the world alongside other races, tend to be fairly "average". They are competitive enough to have survived, but not so overly capable as to have wiped out the other races. Humans tend to be among the most dangerous opponents any race can have; intelligent enough to be dangerous, with short enough lives to be willing to risk a premature death, and fast enough reproduction to overwhelm through numbers. Humans tend to live in surface towns and cities, but can make their homes almost anywhere they can survive.
Dwarves: Dwarves are the master craftsmen. Hearty and long lived, the goal of most Dwarves is mastery of a chosen subject. Society is traditional, but those traditions are pragmatic. It is unusual for Dwarves to develop new products, both as a matter of a slightly hidebound worldview, and the fact that it isn't possible to attain mastery of a craft that you just invented. That said, Master Tinkerers DO exist, and specialize in reverse engineering and improving other technology, often human, gnomish, or goblin in origin. Elaborate traditions involving beards (male) and hair (female) allow a dwarf's history to be read by those who know how. Dwarven barbers and hairdressers are among the best in the world, and any noble of worth will have one on staff (both for their skill and their no-nonsense advice). Dwarves traditionally prefer to craft finely made, sturdy subterranean cities, and often rent and expand basements and sub-basements in cities of other races.
Gnomes: Small but hearty, gnomes are masters of invention. Mischievous and friendly, they prefer to live just underground but are plenty comfortable on the surface. An amiable lot, just about anyone without ill intent can get along with gnomes. Gnomish cities tend to be sprawling and shallowly below the surface.
Goblins: Goblins are small, wiry, and cunning. Like Gnomes, goblins are masters of invention. Where gnomish inventions tend towards the quirky and impractical, goblin inventions are brutal and to the point. Goblin humor tends more towards pranks than that of the Gnomes. Goblins prefer to live in underground cities.
Goblins and Gnomes see each other as rivals due to their significant similarity, but rarely come to actual blows over it. Any town with a goblin and gnomish tinker will usually find them across the street, if not sharing a building. This rivalry takes the form of a friendly competition, often involving tiny gizmos and contraptions duking it out to prove who's tech is superior. Disputes between gnomish and goblin cities will often be settled by an agreed-upon meeting of a few war contraptions, the cause of the skirmish usually forgotten by the end of the battle.
Hobgoblins: Where goblins are cunning, hobgoblins are much closer to traditional portrayals of goblins: stupid, violent, and untrustworthy. They breed like rabbits and are typically a nuisance wherever they show up.
Elves: Where dwarves are the masters of craft, elves dedicate themselves to performance. Many are masterful craftsmen, but lack the single-minded dedication of the dwarves. Mages, dancers, even warriors, elves dedicate themselves to a few arts and master them with an inhuman grace. Their lives are extremely long, bordering on immortality in the eyes of shorter lived races, but just as susceptible to premature ends as any other race. This long lifespan gives even greater resistance to cultural drift than that of the Dwarves.
Orcs: Big and muscular, orcs are masters of physical prowess. Innate brainpower is not much different from that of a human, but orcs have shorter lifespans and typically do not invest the same time to study. Impatience and impulsiveness are common characteristics. Most orc designs seem a bit rushed and haphazard, but they work relatively well.
Trolls: Trolls are a larger race, bigger even than the Orcs. Huge, tough, and naturally armored, they're intelligent but often unmotivated. They tend not to favor tasks that require high manual dexterity, but it's far from unheard of to find surgeons, watchmakers, and the like. Their lifespans are similar to those of dwarves, but significantly more relaxed.
Beastfolk: A broad category rather than a species or race, beastfolk are defined as sapient races with more animalistic characteristics. Lizardfolk, catfolk, centaur, naga, and occasional crosses between them, this category is generally not referred to as a whole because of the differences between the various species. Sizes tend to follow the animal component (smaller critters will lead to smaller humanoids), but 7' mousefolk and 4' cowfolk are far from unheard of. Species tend to be functionally similar to humans, with adaptations and preferences based upon their genetics (improved grace, skill at tracking, strength, sense of smell or hearing, flight/gliding abilities, etc).