Genie

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.

Dungeons & Dragons and Pathfinder

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.

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.

Genies are one of the elementals most likely to produce genasi offspring, though Pathfinder also has a specific "genie-born" hybrid, the Suli.

Changeling: The Lost

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.

Warhammer Fantasy

Whilst there are no genies in the setting, Tzeentchian Greater Daemon, the Lord of Change, has been known to act as one - and, of course, always in a jerkass fashion.

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 bound 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.