This is a subject of great interest to me, on a great many levels. Because of this, there are a great many ways I can answer this question, so I will hit the first few that pop into my head.
First: What seperates what is called "fantasy" and "science fiction" (and I would also add "horror" although as Joshua said about "fantasy" you can have just about any kind of "horror" as long as its scary or unsettling), from "normal" fiction (Defined as fiction in which nothing happens that doesnt/cant happen in "real life") is that "fantasy" stories are truer stories, in the ways that matter. They tend to deal more with bigger, deeper, more genuine things than "normal" stories, which are often all surface and no substance.
As in the wonderful Jane Yolen quote in a previous post, those genres and especially "fantasy" and "horror" bring out the fundementals of things, which are generally what really matter...good and evil, love and hate, faith and disbelief, and the basic things we all deal with..figuring out the right thing to do, why we're here etc.
Personally, I find most "mainstream" stories, those without elements of magic or the like, very superficial, and far less realistic in terms of how the world and peoples real hearts work than most fantasy. There are exceptions, extremely well told stories of the more "normal" sort. Most of the exceptions are either semi historical family type stories like the Anne of Green Gables stories, or dark satirical type stuff.
More simply the basic obvious differences have already been stated. fantasy/sci fi contains elements which (supposedly) do not or do not yet exist in the reality we know, and they tend to be more about the setting, or the big events going on in the story, than individual characters. Characters in fantasy/sci fi stories are usualy working toward some large goal to help/save/preserve whole worlds or large groups of people, most "normal" stories are dealing primarily with the personal problems of the main character or the main character's family or friends. Supernatural horror tends to depart from that somewhat...many horror stories essential involve a single protaganist or small group of protagnists simply trying to survive whats going on, but some times there is a greater aspect to it such as in Stephen King's IT where they wanted to destroy IT for the sake of the whole town of Derry.
I agree with those that have said that trying to define stories through genre is often not terribly effective. In the end as I think someone else said your basically going to have good meaningful stories which draw of archtypes, mythic cords, and underlying truths, and crappy superficial stories that...well...dont.
Its been my experience though that there are more stories with supernatural/superscience/surreal content that draw off those wells of good storytelling, than those that try to stay in the "real world"
