More than 90% of Human DNA Is Useless 'Junk,' Study Finds
mashable.com
mashable.com
Wikipedia seems to agree: "The Encyclopedia of DNA Elements (ENCODE) project[3] suggested in September 2012 that over 80% of DNA in the human genome "serves some purpose, biochemically speaking".[4] This conclusion however is strongly criticized by other scientists,[5][6] with a recent article claiming that "8.2% of the human genome is likely to be functional, while only 2.2% has maintained constraint in both human and mouse since these species diverged".[7]"
Another way to look at it: pick a model organism (maybe c elegans), run many experiments in parallel, finding regions which can be removed and allow viability under a wide range of inducible environments (if you remove the heat shock proteins, but never put the worms in a hot environment, you might conclude you increased fitness). Find the largest regions you can remove independently, then start with pairs of regions (you can imagine that removing region 1 and region 2 independently would have no effect, but be fatal if combined), etc.
The resulting genomes would probably still contain regions that contained no recognizable function, have no strong selection pressure, and yet still be completely necessary for viability. This is just speculation on my part, though.