The links on the prompt titles will take you to
Wikipedia if you want more specific than what the description here is. A link was only added for the trickier concepts that people might not be familiar with.
For the claims such as "pirate," if you claim a pairing or general series, only one of them needs to be the pirate. So if you claim a pairing, one can be the pirate that kidnaps the other and dirty things ensue. :P
Apocalypse:end of the world, not necessarily religious.
Arabian:think
One Thousand and One Nights: Aladdin, Ali Baby and the Forty Thieves, and The Seven Voyages of Sinbad the Sailor.
Bangsian:genre of fantasy set wholly or partially in the afterlife.
Bourgeoisie:claim is upper class or newly rich.
Celebrities:claim is a famous actor, musician, athlete, etc.
Cyberpunk:scifi based on technology i.e. The Matrix and I, Robot.
Daemons:in the His Dark Materials sense where an animal familiar is the manifestation of the soul.
Detectives:claim is a detective.
Eastern:a story with Asian influence or aspects.
Explorers:claim is discovering new places and things whether it be on land, sea, or even space.
Fantasy:elves, fairies, unicorns, and other magical/mystical elements like in fairy tales.
Fourth wall:your claim interacts with its audience (i.e. Batman somehow ends up in our world where he's a fictional character, not a real superhero; if your claim is RPF, they could be the ones meeting Batman when he ends in our world).
Genderfuck:genderbender, androgyny, MPREG, crossdressing, male effeminacy, female masculinity, etc.
Gold diggers:claim is a gold prospector or another type of buried thing-of-value seeker (i.e. miner, oiler, archaeologist/paleontologist, treasure hunter).
History:incorporation of your claim into a real historical event (i.e. War of 1812 but not the Clone Wars).
Hustler:technically a male prostitute but a scam artist will also work.
Infinite cycle:situation the same in the end as in the beginning.
Inmates:claim is a prisoner.
Jocks:claim is an athlete, famous, varsity, or otherwise.
Jossverse:crossover/fusion with any Joss Whedon work (i.e. Buffyverse, Firefly, Dollhouse, Dr. Horrible's Singalong Blog).
Kidfic:claim is a kid or has kids (so, yes, MPREG can be included here).
Killed:can be set during the fandom of your choice but the character dies.
Legends:similar to fantasy but now with the inclusion of folklore.
Lost world:a world out of time, place, or both.
Military: claim is a soldier.
Mutants:claim is mutant with superpowers.
Noir:stylish Hollywood crime dramas that often emphasize moral ambiguity and sexual motivation.
Normal:non-AU piece for your claim. Non-canon aspects such as slash are permitted, but this prompt would be a piece that fits within the show or movie.
Outerspace:spaceships, other planets, and endless starscapes.
Olympians:claim is a god or demi-god.
Pirates:claim is a pirate.
Prehistoric:anything before written word.
Quest:claim goes on a quest.
Quetzalcoatl:incorporation of your claim into any myth.
Regency:masquerade balls and a time of excess for aristocrats.
Royalty:kings, queens, knights, and all that was medieval times.
School:a story taking place in high school or college.
Steampunk:fantasy based on steam becoming the main source of power for technology, i.e. dirigibles and locomotives.
Telepaths:the ability to sense the thoughts of others; psychokinesis (affecting objects with the mind) will also be accepted for this prompt.
Thieves:claim is a thief.
Urbanites:claim lives in the city.
Utopia:the "perfect" society i.e. Equilibrium and 1984.
Vampires:claim is a vampire.
Villains:claim is the antagonist.
Western:cowboys, horses, shootouts, and lots of leather.
Wizards:claim can use magic.
Xenogenetic:claim was adopted or raised somewhere different from canon.
Xover:crossover with a fandom of your choice.
Yeomen:claim is a farmer or a servant/peasant in the Middle Ages.
Yuppies:young urban professionals.
Zombies:claim doesn't have to be undead but at least fighting them.
Zoomorphs:claim can morph, get changed into an animal, always have been an animal, or be anthro so they're normal except for some characteristics like cat ears and a tail.