Far it be from me to incite the 9,854th debate about the relative superiority of Jeannie and Samantha, or their respective shows. I love them both. I will say, though, that the setup of Jeannie has always made more sense to me. Unlike Darrin on Bewitched, Tony Nelson never much cared if his sparking clean house and fabulous dinners were conjured up with magic, and he didn't pitch a hissy every time Jeannie blinked. I'm pretty sure I'd feel the same way about it, just in case I should ever have the opportunity. Let's face it, whether your reasons are punitive, practical, or prurient, most of us would take advantage at least once in a lifetime of the chance to say to your personal genie, "Blink out their clothes!" (See season 5 episode "Jeannie, the Recording Secretary" for details).
When I was ten or eleven years old, reruns of both Bewitched and Jeannie played every weekday afternoon on Channel 5 in Atlanta, where we lived. Much to my frustration, however, either the syndication package at that time didn't include the black-and-white episodes, or the station chose to skip over them. It was probably an ominous foreboding of my future as a TV historian that I once begged to be allowed to stay home from the beach one afternoon on a family vacation, because the local station was going to show the Jeannie pilot episode, which I'd never seen. Belated thanks, many years later, to my parents, who (I think) sorta understood.