Genies, a term corrupted from the Arabian term "djinni", are mystical spirits best known for their immense magical powers, which iconically allow them to literally alter reality as they see fit. Because of this, mages have a pretty long tradition of magically stuffing them into small objects (lamps are most iconic, but rings and vases are pretty common too) and compelling them to obey whoever holds their prison. They also tend to be major league dicks, though whether this dickishness is because of the aforementioned "being stuck in a lamp and forced to grant wishes for every yahoo who can get ahold of it" or they got stuffed into a lamp for being a dick tends to vary.
They're usually pretty good looking, and it's not unheard of for them to have sex with or even marry mortals.
Genies are one of the "big names" for the Elemental Planes; being the most human-like in appearance and intelligence, they present a "face" for interactions both positive and negative that the more primordial elementals lack. There are four species of genie, one for each of the four major elements; Djinn (air), Efreet (fire), Dao (earth) and Marid (water). Although very different in personality, the four types each share certain traits, including polyamory and large libidos, vaguely Middle Eastern cultures, and the ability to grant wishes with a laundry list of restrictions (notably, they can't grant wishes for themselves or other genies, and while they can grant one wish a day they can't grant another wish to the same creature until a very long period of time has passed).
Some versions of the game also state the existence of a 5th "mixed element" genie tribe called the Jann, who are the weakest of their kin.
Of these four races, it has always been the Djinn and the Efreet who have stuck out the most in the D&D player's mind. These two races have very clear archetypes; djinni are the "friendly leaning but dangerous if made moody" genies, whilst efreeti are the "obviously evil genies". In comparison, dao tend to boil down to "efreeti with earth powers and a lot more greed for gold and gems", whilst marids tend to boil down to "djinni with water powers, an even more fickle attitude, and a barrowload of extra ego".
In fact, it got to the point that 4e originally left both races out; it wasn't until an article in Dungeon Magazine #199 that the dao and marids both returned to 4th edition. And they were still pretty much identical to their classic depictions; dao were avaricious, evil, giant earth-genies obsessed with mineral wealth, and marids were arrogant, flamboyant, adventurous water genies who all to the last claimed a noble title. Whether this was deliberate - a lot of the later 4e Dungeon & Dragon magazine articles tended towards bringing back older lore - or was just a sign that the grid-filling nature of D&D genies robs even the best authors of their creativity, who can say?
Al-Qadim, the "Arabian Nights" mini-setting for the Forgotten Realms, placed a lot of emphasis on genies, naturally. It created the "Tasked Genie" designation, a variety of lesser genies specially molded to fulfill certain tasks until they had become entirely new species revolving around that task (specific strains: Administrator, Architect/Builder, Artist, Deceiver, Guardian, Harim Servant, Herdsman, Messenger, Miner, Oathbinder, Slayer, Warmonger and Winemaker). It created the Markeen, or "Genie Double", a genie cursed to be the exact physical replica of a mortal, and it introduced the Sha'ir class; a Wizard variant that drew its powers from the service of a minor allied genie called a gen.
3.5's Tome of Magic introduced a new breed of genie; the Khayal, a "darkness elemental" genie native to the Plane of Shadow. Master wielders of shadow magic, khayal are distinguished by their dark, dusky-gray skin and their utter-black eyes, which appear more like night-filled holes in their skull than anything human-like. If one can look past that, they otherwise look like slightly taller than average humans. They regard the other elemental genies with varying levels of antipathy, but have an especial hatred for jann. Looking down on all other races, khayal culture revolves around deciving and manipulating them - although they are never anything but scrupulously honest with each other. Tradition holds that anyone who can irrefutably prove they have been lied to by a khayal is owed a single task from that genie in recompense, but they don't always live up to this. They have been known to assist mortals of their own volition, either out of mutual need or due to being impressed at the mortal's deceitfulness, but they display archetypical genie arrogance when they do.
It's quite possible for a changeling - or, more fittingly, a True Fae - in Changeling: The Lost to style themselves after a genie. In fact, the splat Night Horrors: Grim Fears actually features a genie-motifed magically bound True Fae called Ybalashi, who is compelled to grant the wishes of whoever holds her vessel. Of course, as her title of "The Artisan of Poisoned Desires" suggests, making use of her magic isn't a smart thing to do.
For example, in one old Warhammer comic, an imprisoned Lord of Change was set free by three travelers. In "appreciation" for them setting it free, he would each give them a wish. The first wanted the ability to fly, and the Daemon turned him into a fly. When the two complained, it defended itself by claiming that he wasn't specific enough. So the second wished to live forever, and the daemon turned him into a vampire, which then forced the third companion, a Dwarf, to kill him. The dwarf, seeing that the Lord of Change would obviously screw over any wish it will grant, did the brilliant decision of making a wish that he was worth his weight in gold.........That worked just as about as well as you might expect since the daemon then turns him into a statue of solid gold.
Meanwhile, over in Mordheim, the mercenary Nicodemus was a wizard's apprentice who foolishly freed a bounded Lord of Change and then wished to be "the greatest wizard in the world". This caused him to start growing into a giant spellcaster, and he was forced to come to Mordheim for a steady supply of the wyrdstone he needs in his growth-retardant potion. There's even a fan adventure where he runs out of potion long enough to grow to the size of a real giant.