Bewitched. The premise seemed too much like a Playboy fantasy: astronaut Tony Nelson (Larry Hagman) finds a bottle washed up on a beach, opens it, and out pops a genie -- nameless, so he calls her Jeannie (Barbara Eden). She calls him Master. She wears a belly-dancing costume that leaves little to the imagination, and is willing to do anything he wants. Anything.
To his credit, Tony doesn't take advantage of the situation. Like Darren of Bewitched, he wants to take care of himself, and he forbids Jeannie from using her magic (she, of course, disobeys him). His best friend Roger (Bill Daily) is less scrupulous -- he can think of lots of things to wish for.
According to Barbara Eden's autobiography, Rorke (here with gay icon Judy Garland) was "unashamedly gay" in real life, and "a prince" who often invited cast members to dinner parties at his home.
After Jeannie, Larry Hagman went on to Dallas, of course, and Barbara Eden chose roles involving gutsy, go-getting women to prove that she wasn't just a belly-dancing sex object.
She reprised her Jeannie character twice:
I Dream of Jeannie: 15 Years Later (1985) substituted Wayne Rogers of M*A*S*H for Larry Hagman, who was busy with Dallas. In order to save Tony's life, Jeannie has to sacrifice her relationship with him -- and he must forget that he ever knew her.