The following is a list of those gods named so far which could be considered small gods or household gods:
Big Rat Underground
The creator god somewhat hazily conjectured by the Clan in The Amazing Maurice and his Educated Rodents. Some of the Clan believe that if a rat has been a good rat, then when the Bone Rat comes, he will take them to the Big Rat, who has a tunnel full of food. Most of the rats who think about this are continually questioning it, so it's not clear if there is enough belief for a god to form. Still, one rat's near-death experience seems to suggest there may be something similar to the Big Rat Underground waiting for the Clan beyond death.
The "Oh God of hangovers". His reason for being is to feel the after-effects of drinking, instead of the god Bibulous (the Discworld's Bacchus). He is one of the characters who appears during the events of Hogfather, due to there being a lot of unused belief floating around.
Thanks to the wizards of the Unseen University Bilious' symptoms are reversed for a time and he is able to help Susan on her quest (and make Bibulous feel thoroughly miserable. After all, everyone knows a good hangover cure has got to involve a lot of humorous shouting, et cetera, and this one was made by wizards; however, since Bilious always receives Bibulous' hangovers, the negative effects of the cure are transferred in the opposite direction). While most of the beings created in Hogfather disappeared at the end, it is possible he remained because of the belief that Violet (a tooth fairy) had in him, in which case he may have begun a relationship with her, and started a career as a temp-worker for gods that want a holiday. Or, alternatively, since it is impossible to die in the Tooth Fairy's Castle, he could still be there as he is unable to vanish from lack of belief.
Bilious appears in the TV version of Hogfather played by Rhodri Meilir.
A "rather liberal" god in the opinion of Constable Visit, "not big on commandments". His followers died out fighting some of the most gruesome wars in the history of the Unnamed Continent. An excerpt from the Cenotine "Book of Truth" was the Chem of the golem Dorfl, until Carrot Ironfoundersson purchased him and set him free by replacing it with the receipt of the purchase.
The goddess Czol was an ancient goddess of Thut before that land sank under the sea some 9,000 years ago. One does not ask about her. Mentioned in Going Postal on a list of things that a messenger can't deal with. She is an ancient form of Mrs. Cake.
The Howondalandish tribe of this Goddess believed that their ancestors resided in the Moon. After a signal from their ancestors (an unusually large flare from the Moon) they were urged to kill anyone who didn't believe in Glipzo. Three years later the tribe was destroyed by a rock falling out of the sky, as a result of a star exploding a billion years before. Mentioned in The Last Hero.
God of Evolution
The paradoxical God of Evolution appears briefly in The Last Continent, where he is found 'sculpting' animals. Since he hasn't figured out reproduction yet, he makes every animal unique.
Although no-one believes in the God of Evolution, he survives thanks to his own strong belief. He does not believe in himself, because he is an atheist, but he believes in what he does. During events detailed in The Last Continent, he briefly takes on Ponder Stibbons as an apprentice, but scares him off when he reveals his most perfect creation to be the cockroach. This may be a reference to the real statement of J. B. S. Haldane that "God must have inordinate fondness of beetles". He subsequently appears in The Science of Discworld III: Darwin's Watch, where he is inadvertently responsible for a lot of confusion. The God of Evolution exists in part to parody the concept of Intelligent Design.
The Goddess of Shoes. She has a small following that gathers in the Temple of Small Gods and worships the Sacred Lace of Hyperopia. Mentioned in Reaper Man and Discworld Noir. Named after the technical term for long-sightedness, and it is possible that she is inspired by the Greek goddess Nike, and the shoes named after her.
The Goddess of Interminable Opera. She is one of the many gods and goddesses recognised in the Temple of Small Gods. Mentioned in Discworld Noir.
Nuggan is the locally worshipped monotheistic and omnipotent God of Borogravia, but elsewhere he is known as the God of Paperclips, Correct Things in the Right Place in Small Desk Stationery Sets, and Unnecessary Paperwork. He usually sports a fussy little moustache.
His holy writ (the Book of Nuggan) is a Living Testament, into which more material is added on a regular basis. All believers regularly add pages to the ring binder Appendices, which then eventually fill with more commandments, usually Abominations unto Nuggan. By the time of Monstrous Regiment, his commandments were becoming rather nonsensical — among his ever-growing list of Abominations were cats, the colour blue, Dwarfs, oysters, mushrooms, chocolate, garlic, babies, cheese, the smell of beets, ears, jigsaw puzzles, crop rotation, shirts with six buttons, and rocks. He is also very opposed to the clacks system, as it interferes with the prayers of the faithful.
His existence is the basis for Monstrous Regiment and he appears in The Last Hero. He is now dead because belief has switched to his abominations, similar to the events leading to Om's weakening in Small Gods.
The God of a Howondalandish tribe which wiped out the nearby N'tuitif tribe at his signal (an unusually large flare from the Moon). Shortly after, this tribe was also wiped out by another tribe who worshipped the goddess Glipzo. Mentioned in The Last Hero.
Thousands of years ago this god was a major competitor against Om. The god now being completely forgotten by humans, only Om recalls the existence of Ur-Gilash. As a small god, he may have been encountered by Om while the tortoise-god was crossing the desert with Brutha. Om and Brutha came across a small god who knew genuine god-speech, which was such a rarity that given the location, Om reasoned that it was once Ur-Gilash himself. Mentioned in Small Gods.
The term "demon" is essentially interchangeable with "god" on the Discworld. It is even possible for some to be both at the same time. Pratchett explains the difference between them as being essentially the same as that between "terrorists" and "freedom fighters".
Astfgl is a Demon Lord, appearing in Eric. At the start of the book he has been made King of Hell, and his modern, go-ahead attitude is driving the other demons to distraction. In particular, Astfgl believes demons should operate Hell and extend themselves to the Discworld by creating such instances of extreme and inescapable boredom that the human brain turns to mush and the condemned soul realizes there are worse things than eternal pain (Particularly since they don't even have bodies any more and hence can't actually feel pain unless they want to). By the end, thanks to the machinations of his more old-fashioned rival Vassenego, he is "promoted" to Life President of Hell, a job that consists of writing "policy statements" while Vassenego rules in his stead.
Imps are tiny demons that perform minor tasks rapidly (similar to Maxwell's demon). A number of Discworld labour-saving devices exist which function by trapping small imps (it is implied that they are made using magic, and in Making Money they are described as a "living spell", but small 'wild' demons have also been used). The most notable is the iconograph, but others include watches (The Colour of Magic, Reaper Man, Thief of Time), food processors (Nanny Ogg's Cookbook), razors (Thud!) and personal "dis-organisers" (Feet of Clay, Jingo, The Truth, Thud!).
The imps in these devices seem not to mind their jobs, although they get sarcastic if overworked or asked to do things outside their purview. They also seem to lack imagination making them (theoretically) more reliable to do things correctly.
A neuralger is a female demon which comes to men in their dreams and has a headache at them. They are usually summoned by mistake, by demonologists who were expecting a succubus. The Neuralger is mentioned in Eric, although a similar concept appears in Pratchett's (non-Discworld) drabble Incubust. From Neuralgia the medical term for a painful disorder of the nerves often resulting in severe headaches.
While being basically a demon of relatively low rank, Quezovercoatl (also known as The Feathered Boa), was the god of Human Sacrifices in the Tezuman Empire's state religion. He appears in Eric and is described as half-man, half-chicken, half-jaguar, half-serpent, half-scorpion and half-mad (a total of three homicidal maniacs). Because his physical form was some six inches tall in real life, he had relied on appearing in visions to guide his followers. Conversion was probably sped by the bloodthirsty nature of his religion and the fact that the Tezumen were at the time worshipping a stick. Eventually he was forced into appearing physically by Astfgl, whereupon he was trampled by The Luggage. After some time spent worshipping the Luggage, to no avail, the Tezumen finally killed off their priests and settled for atheism. His name is a portmanteau of the Aztec god Quetzalcoatl and the word "overcoat".
The Great God of the Strict Authorized Ormits. He can usually be found residing in one of the Nether Hells. As of the Year of the Cobra there are only two known worshippers left; a student assassin (Arthur Ludorum) and his mother.
The correct worship...