We've pretty much settled on science fiction as being the best name for the sort of stuff we in genre like to read and write. Is it really the best possible term? Probably not. But, as with democracy, before we get too critical, we should probably consider the alternatives.
Going back to the beginning, Jules Verne wrote Voyages Extraordinaires, emphasizing the adventure aspect of his fiction. H. G. Wells, a far better prose stylist but a little looser with the laws of science -- when asked his opinion of Wells' First Men in the Moon, Verne snapped, "Show me this cavorite! -- wrote what were then called Scientific Romances. (The term predates him, but I'm not pretending to any rigorous scholarship in this blogpost.)
Then came the tireless science enthusiast, inventor, and crook, Hugo Gernsback, whose magazines created science fiction as a genre and whose letter columns in those same magazines created fandom. In keeping with the aesthetics of a man who named his weirdly visionary novel Ralph 124C41+ (try saying it out loud), his moniker for this nascent literary form was a real jaw-acher: Scientifiction.
Obviously, that couldn't endure and with the demise of Gernsback's magazines, the acceptable term among cognoscenti became Science Fiction. Shortly thereafter, the abbreviation SF came into common insider use, sometimes capitalized and other times not.
Alas, uber-fan, agent, magazine editor, and compulsive collector Forrest J. Ackerman, seeking his place in literary history, came up with something shorter and catchier: Sci-Fi. It caught on. Sort of. Mostly, it became attached to 1950s monster movies. Fans pointedly used "science fiction" to refer to the sort of literature they valued, while reserving Ackerman's term for schlock. Thus causing a great deal of snarking by those in the know directed at innocent civilians who thought they were simply using the proper term.
(Not long ago, the SciFi Channel, whose name roused outrage in fandom when it first came out, officially changed their name to SyFy, a Polish word meaning "syphilis." Their intention being to distance themselves from the schlock implications of the old term. Which was ironic, given how greatly many of its own shows contributed to exactly that impression.)
Somewhere in there, Robert A. Heinlein made a valiant effort to point out the inherent virtues of the genre by giving it a more respectable title: Speculative Fiction. This had the virtue of getting around the fact that a lot of the works we most highly prize, such as Ray Bradbury's, while excellent on the speculative front, weren't terribly strong on the science.
Alas, though Harlan Ellison spent decades championing this term (and excoriating the use of "sci-fi"), it never caught on among the general public. So it must be considered a failure. If Harlan couldn't make it stick, nobody could.
Today we have, through attrition and the will of the masses, settled upon Science Fiction as the one true name for our beloved genre. Just in time, as John Clute would tell you, for its death.
But that's another story, for another time.