Aztec
The Aztecs were one of the three great empires that ruled over the lands now called Central and South America prior to the arrival of Europeans, alongside the Mayans and the Incas. The best-known of the three (until Eric Thompson bit it and the scholarly world finally accepted the Proskouriakoff - Coe Maya decipherment), the Aztecs were the overpower of modern-day Mexico. They arose from humble beginnings as a single Nahua tribe called the Mexica, who came down south to modern-day Mexico from an unknown area to the north called Atzlan. They formed an alliance with Texcoco and Tlacopan (now "Tacuba") to rule a vast empire of subordinate vassal-states; through their diplomatic, trade, and ultimately martial skills. The Mexica and Texcoco sidelined Tlacopan fairly early on; at the end, Moteczoma II subjugated Texcoco under a puppet ruler and was in the process of absorbing it all when the Spaniards came knocking.
The Triple Alliance oversaw a highly advanced and cultured people, if you grade on a Chalcolithic curve. The Mexica / Aztec side had elaborate skills in architecture, sculpture, ornamental metalwork, and warfare; as well as skilled in trade - the pochteca system. Texcoco maintained the lore of Central Mesoamerica and composed much poetry of its own, most of which survives to this day, having impressed even the Catholics. All Mesoamericans were highly spiritual, whose culture was largely shaped by their religious devotion, although as the Mexica in particular interpreted that - well, read on.
The Mexica religion has gone down as perhaps the single bloodiest faith in human history. Blood sacrifice, up to and including that of humans, has been practiced by religions around the world pretty much as long as the concept of religion has been a thing, but the Aztec pantheon was uniquely bloodthirsty, starting with the central precept that human blood was of vital spiritual importance as the fuel that kept the universe working. Even basic offerings to the gods most frequently took the form of the Aztecs drilling into their arms, thighs, ears, lips, tongues and dicks with thorns and offering the bloody thorns. A traditional fertility rite to increase the productivity of a field was to tie a captive warrior between two trees and then riddle him full of arrows - the objective explicitly being to kill him as slowly as possible to ensure more of the blood went into the field. Tlaloc the Rain God was propitiated by ceremonially torturing and then drowning children. To evoke the favor of Xipe Totec, the Harvest God, priests would flay sacrificed virgins alive and wear the skins as ceremonial raiments to perform dances in. And, of course, Huitzilopochtli, patron god of the Aztecs, was offered hearts cut from the chests of living victims.
This fueled the warlike nature of the Aztecs, and was responsible for their uniquely styled empire - the Aztecs "proper", the Mexica people, inhabited a single city-state that was supported by two sub-ordinate city-states, and ruled over a vast quilt of conquered tribes and city-states. To get the sacrifices they needed, the Aztecs would fight ceremonial "Flower Wars" against vassal states and real wars against peoples on their borders. Which of course meant people didn't like them much. Seriously, the Aztecs inherited most of their gods from their neighbors (barring Huitzilopochtli, who was uniquely theirs), complete with the traditions of human sacrifice, and their neighbors still thought they were a bunch of blood-soaked fanatics. So, when a tiny Spanish Conquistador exploration fleet showed up, they succeeded in "conquering" the Empire in large part because the vast majority of the Empire and its surrounding neighbors threw their lot in behind the Spanish to get rid of the Aztecs.
Fantasy Aztecs
The Aztecs and their unique combination of military imperialism, being a theocracy devoted to malevolent-seeming gods, and religion based on Blood Magic, have been something of an inspiration for fantasy games for a fair amount of time.
In Mystara, the Tiger Clan of the Atruaghin is a relatively "benign" depiction of the Mexica; they've dropped the human sacrifice thing, but are still a bunch of brutal war-loving racial supremacists who serve as the Evil Faction to the Mesoamerican-based Atruaghin Clans. The Hollow World has the Azcans, who are the even-more-evil counterpart to the Tiger Clan and who do practice human sacrifice, as well as having more of the Aztec visuals. The Schattenalfen are an evil Shadow Elf offshoot who've picked up some Aztec traits, namely the human sacrifice thing. All three groups worship the same malevolent Mystaran Immortal; Atzanteotl.
In the Forgotten Realms, the sub-setting Maztica is basically Aztec Mexico with a dash of magic added to the top of it. It even emulates the whole "most of the Aztec empire didn't actually want to be Aztecs" thing; the truly devout worshippers of the bloodthirsty Zaltec are restricted to the peoples of one city-state, Nexal, who suffered for it when their god actually came to the Material Plane and his presence transformed them into orcs and ogres, resulting in the toppling of their empire and the resurgence of the long-buried Qotal faith.
In Shadowrun, the Megacorp Aztlan is based on the idea that a bunch of Southern Mesoamerican peoples got together and became a Megacorp deliberately styling itself after a mixture of Aztec, Mayan and Incan influences. Their unique gimmick is their heavy usage of Blood Magic.
In Deadlands Classic, there's a hidden kingdom of Aztecs who survived the Conquistadors in the deep jungles of South America and they've been plotting revenge ever since, which they hope to achieve with Blood Magic and an army of zombies. Naturally, the Reckoners love them.
In Magic: The Gathering, the civilizations of Naya, the Red/Green/Black Shard of Alara, have a certain level of Aztec motif. Meanwhile, the Sun Empire of Ixalan combines elements of Aztec and Inca.
A Word of Caution
Let's get something straight here: the Mesoamerican people suffered a lot of terrible shit at the hands of European settlers. There's no arguing with that. Colonialism sucked. But that doesn't mean they couldn't also be dicks in their own right. And the fact that the Aztecs' own "empire" revolted to overthrow them when the Spanish showed up is pretty blatant evidence that they were a bunch of crazy fanatics even by the standards of their own people. But since SJWs became a thing, it's become a risky gambit to ever have Mesoamerican-inspired characters or cultures in an antagonistic role, and the Aztecs are no exemption.