This isn't that difficult of a question for me, as there are really only two contenders for the position of my favorite genre: fantasy and science fiction. And while I love them both, star ships and aliens beat out wizards and elves by a narrow margin.
I love fantasy. Among the earliest genre novels I read were classic works of fantasy like J.R.R. Tolkien's Lord of the Rings, C.S. Lewis' Chronicles of Narnia, and Lloyd Alexander's Chronicles of Prydain. I love Moorcock's Eternal Champion books, Zelazny's Amber books, and I even have a soft spot of Eddings' Belgariad and Donaldson's Thomas Covenant books. Fantasy fiction, when written well, connects us with the myth and folklore of our history. It offers us a window into the storytelling rhythms that have resonated down to us from the past, and will probably continue to resonate forward as long as humans tell each other stories. Plus, it is fun to read about bold warriors, crafty thieves powerful wizards, ruthless villains, and terrible dragons.
But science fiction looks the other direction, to a world of future possibility. The genre looks at humans and tries to decide what the full range of possibilities might be, even if those possibilities are actually, due to the constraints of physics, impossible. To a certain extent, some science fiction novels, like Frank Herbert's Dune books or Edgar Rice Burrough's Barsoom series, walk the line between science fiction and fantasy. In that regard, one might say that science fiction encompasses a fair amount of fantasy, and so by choosing science fiction as my favorite genre, I'm cheating a bit because I get a big chunk of fantasy as well. But the line between genres is blurred and indistinct no matter which ones you pick, so I'm not going to worry about that.
And one thing about science fiction is that the possibilities it explores don't have to be happy. Many science fiction novels take place in an imagined reality that is somewhat terrifying to the modern reader. And in some cases, the terrifying nature of the reality is that this is the best of the possible worlds that the inhabitants could come up with. Or the fictional future is intended to be bleak and awful so the writer can make a storytelling point. This almost never happens in fantasy fiction. I don't think anyone has ever written the fantasy equivalent of Yevgeny Zamyatin's We, or Aldous Huxley's Brave New World. Science fiction has such a wide array of directions it can go: from space opera like "Doc" Smith's Lensman series, to hard science fiction like Baxter's novel Ring, to social science fiction like Le Guin's Left Hand of Darkness, and everything in between and then some.
Because science fiction has such a diverse range, and because it is forward looking, exploring vistas of human endeavor to come, it is my favorite genre.