Once your in the near future then I'm not sure if you can count that as the "real world." "Battlestar Galatica" for example isn't realisitc.
Okay, that's a complete non sequitur, since BSG was set in a totally alien society 150,000 years in the past. I'm talking about something like The Truman Show or a book like Gregory Benford's Eater -- something set in a future close enough to ours that it's indistinguishable except for one or two technological advances or discoveries that are key to the story. A great deal of science fiction throughout the history of the genre has been in such a setting relative to its date of publication, so it's totally wrong to exclude such stories from the definition.
Heck, go back to the earliest works that defined the science fiction genre as we know it, and most of them are set in the recent past. In the 19th and early 20th centuries, the standard conceit for fantastic literature -- indeed, probably for most literature -- was to present it as if it were a true story being related either by one of the participants or by someone to whom the events had been related. This is true of the works of H.G. Wells and Jules Verne, it's true of Shelley's Frankenstein, it's true of Edgar Rice Burroughs' Barsoom novels, etc.
"Fringe" on the other hand feels like something that could be happening right now. It helps that they are working on a college campus instead of some secret underground base and that everyone on the show is a regular human being instead of being a robot or a messenger from God or a clone or a alien.
Exactly my point. There is plenty of science fiction in that "happening right now" -- or 1-5 years from now -- category, and there always has been. And Fringe is obviously not in the real world -- it's in a similar fictional world where a company called Massive Dynamic dominates many industries, where the level of technology achieved by Massive Dynamic and other, private developers surpasses real-world technology by a considerable degree, and where the laws of physics and common sense are far more loosely applied (for instance, it is possible for an organism to grow from an embryo to a full-sized adult within minutes without consuming any food as a source of biomass and without burning up from the heat of its own metabolism, thus grossly violating more than one fundamental conservation law).
For that matter, no fiction is set in the real world. In the real world, there's no Dr. Frasier Crane with a radio show in Seattle. In the real world, Jack McCoy isn't the district attorney of New York City. In the real world, CSI personnel don't interview suspects and solve the cases all by themselves. In the real world, people who leave their front doors unlocked have home invaders and burglars barging in, not just wacky neighbors. In the real world, cars don't blow up unless they have actual bombs in them. All fiction departs from reality to a greater or lesser degree.