The world of Ghosts 'n Goblins is host to a wide variety of video game.
The core Ghosts 'n Goblins series is known as either Ghosts 'n Goblins, Ghouls 'n Ghosts, or singularly referred to as Makaimura in Japan, which translates to Demon World Village. There are 4 games that are definitive successors to the main game: Ghosts 'n Goblins, Ghouls 'n Ghosts, Super Ghouls 'n Ghosts, and Ultimate Ghosts 'n Goblins. The first two being released for arcades first, (unique hardware and CPS-1, respectively) but are more famous for the NES port of the former and the Genesis port of the latter; then the third was made uniquely for the SNES and the forth for the PSP.
There are also games arguably just as much part of the series, but are relegated to secondary status for their obscurity: Makaimura for Wonderswan, Ghosts 'n Goblins: Gold Knights I & II, and Makaimura Online. Arthur to Astaroth no Nazomakaimura: Incredible Toons is little more than a different puzzle game rebranded to fit the series, but carries the Makaimura brand nonetheless.
The first game is a cartoonish, gothic themed side-scrolling platformer where the player is able to wield a variety of medieval weaponry near-strictly as projectiles. There can be a certain amount of each projectile on screen at any given time depending on which one is equipped. In this way the gameplay very much resembles the Mega Man series also released by Capcom, which eclipses it in popularity but in which it predates by 2 years. Weapons are equipped by touching them, and since some situations require you to so that you can avoid death, and since it overwrites the previously held weapon, this can cause great frustration, as some weapon types hold clear advantages over others.
The second game added the ability to throw weapons up or down as well as right and left, significantly altering gameplay. The third game added a double jump while removing vertical attacks. The fourth kept both vertical attacks and double jumps, the latter as one of few abilities gained throughout the game - which undoubtedly has the most RPG elements in the franchise.
The most enemy types will continuously spawn, forcing the player to be constantly active to stay alive while the game is not paused. There are few consistent enemy types throughout the series, most notably the Red Arremer - one of which would star in his own series within the same world.
The game is notorious for forcing the player to play through the entire game again in order to face the last boss, get the true ending, and technically beat the game.
As was prevalent at the time, the game features a plot where Arthur has to rescue the princess (Princess Prin-Prin/Guinevere) from her evil kidnappers. These kidnappers are the army of the Demon Realm with an ever-changing chain of command. Satan is a fuzzy gargoyle often shown as the one kidnapping her, but is clearly under the command of another demon. Whoever is the last boss in each game is evidently also the ruler of the Demon Realm at the time, being Astaroth in the first, Lucifer (Loki in the Genesis version) in the second, the Demon Emperor Samael/Sardius in the third, and Hades in the fourth. Astaroth appears in all of the games, but after his original defeat he is always a subordinate of the ruler who has taken his place.
While these games exemplify who ranks above who in the Demon Realm by the order which they are fought, the Gargoyle's Quest series serves to exemplify their politics and contrasting personalities with far greater complexity, serving to explain the reasoning behind changes in leadership.
In Ultimate Ghosts 'n Goblins, it is finally revealed why members of the Demon Realm continue to kidnap Princess Prin-Prin: she is the last human in the game's world with royal blood in her veins, and she is sought because if her blood is mixed with that of a demon's through precarious means, it would give the Demon Realm control over the Human Realm.
This series consists of Gargoyle's Quest, Gargoyle's Quest II, and Demon's Crest. While it would be easy to mistake these games as another series at a glance in the West, each of them are given the subtitle Makaimura Gaiden in Japan, solidifying them as part of the same series. The protagonist is Firebrand, a unique Red Arremer, in the same Demon World that the other Makaimura games take place in.
The core of the gameplay takes place in sidescrolling stages not unlike Ghosts 'n Goblins, though with very different mechanics due to the different main character. However, unique to this series is an overworld and NPCs to engage with, giving it quite a bit of non-linearity. This mix could be compared to the gameplay style of Zelda II. The first two games also feature Final Fantasy-like overhead towns to visit with many NPCs to interact with, random encounters in the overworld, and abilties which can be leveled up. The third has Firebrand soaring over the overworld rather than walking through it, ditching random encounters and large NPC filled towns while retaining the option to complete levels in whichever order the player chooses, abilities that are gained through the pursuant progression, and dialogue with NPCs (though much more sparse).
The chronological order of the games is Gargoyle's Quest II, Gargoyle's Quest and Demon's Crest last.
Interestingly, the ending of Gargoyle's Quest has Firebrand "rewarded" with the choice to oversee humanity in the Human Realm, as they have just been created. He is offered the right to conquer this realm if he wants, which he presumably turns down, though this is never explored further. This likely places these games thousands of years prior to the core Ghosts 'n Goblins series.
Demon's Crest however occupies an unknown chronology. The main antagonist, Phalanx, mentions that he lost in battle against Firebrand a thousand years prior. Thus he is likely to have existed at the time of Ghosts 'n Goblins, whether or not he actually appears in the games as one of the Red Arremers encountered.
The Maximo series has been stated canonically (and not refuted) to take place within the Ghosts 'n Goblins series. While not directly tied to any of the other games, obvious similarites include a reminiscent cartoonish art style, a gothic world and enemies, wearing nothing but heart-pattern boxers when you are hit, to even using the main Ghosts 'n Goblins theme in certain areas. They are the only fully 3D games to take place within the universe.
Maximo is a king betrayed by his aide, Achille, who has kidnapped his love Queen Sophia and forced her to marry him, and has also harvested souls of the underworld to create his own army of the undead. Upon trying to rescue Sophia, Maximo is killed, but is brought back by Death whose job is threatened by Achille's actions causing the loss of the dead. The sequel deals with Maximo searching for Sophia, and is interrupted by the Zin - an ancient army of robot-like creatures powered by lost souls.
It is notable that, while the Ghosts 'n Goblins characters are named after ones of Arthurian legend, the characters of Maximo are loosely based on figures in Greek/Roman history. If based on real world chronology at all, this would logically place the Maximo series in a time period prior to the main Ghosts 'n Goblins series.
Also, bosses in the original games are most often named after either biblical demons or demon-like creatures from world mythology, while the bosses in Maximo are simple ghoulish names such as "Ghastly Gus" and "Lord Glutterscum". It is unknown how much these creatures (if at all) are related to the Ghoul Realm. Due to the lack of commonality, and the explanation behind the presence of all the enemies in the Maximo games, it would seem this story arc only documents the evil which occurs within the Human Realm of the same universe.