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Hey, we've seen Superman do it. We've seen David Blaine do it (and then have Chris Angel subsequently show us how he faked it, of course). Of course, Regan floats during her exorcism as well.
And that's all well and entertaining, but physics has pretty much ruled out levitation as a scientific capability. Well, sort of.
There is still a working theory as to how to get oneself literally 'head-over-heels.' And there have been a few notable occurrences of objects (not people) defying gravity. Stick around and you could learn how to change light bulbs without a step-stool, or start hustling basketball like your 1990's Woody Harrelson.
Though, I don't recommend trying this at home…if only because you'll make things really awkward.
Levitation is a metaphysical act of raising an object into the air without the use of illusion, trickery, or a physical process. As such, levitation is a product of psychokinesis-the ability to manipulate objects or events with thoughts. Pyschokinesis itself is largely considered a pseudoscience, and if proven accurate it would refute basic physicals laws like the inverse square law, the second law of thermodynamics, and the conservation of momentum. Essentially, everything we've ever known would be shot to sh!t.
Yet there are a few individuals with telekinetic powers. Nina Kulagina, a Soviet housewife, demonstrated enough paranormal ability during The Cold War to become a concern for the U.S. Department of Defense. Let's not forget that The Men Who Stare at Goats was a real U.S. military initiative.
But because psychokinesis is hard to replicate, and is a rare, innate characteristic amongst the human population, it remains fictionalized. The same remains true for levitation.
Religions purport the most accounts of levitation, regardless of their divine beliefs. Christianity provides the highest number of levitating disciples, with a number of saints granted the power. Hinduism supports the belief that some gurus and masters of yoga achieve the power to levitate via meditation. Yogi Pullavar levitated in front of a crowd of 150 people in 1936, while newspaper reporters were encouraged to take pictures and search the area for wires or other indications of a hoax. None were found.
 Yogi Pullavar levitation, 1936 ...via Weird Asia News
Spiritual mediums are a common source of levitation reports. Daniel Dunglas Home is reportedly known to fly in and out of buildings through adjacent windows. Many mediums face speculations, and Home was not excused from such, though no significant evidence in favor or against his powers was ever lodged.
Yet there remains a scientific theory in which levitation remains fathomable.
Enter the Casimir force. This force has the ability to push together two non-conductive, low-mass metal objects together in a vacuum. All possible wavelengths occur in the vacuum, but only a certain denomination of wavelength is allowed between the objects. The wavelengths between the objects are a smaller infinity than those outside the plates, resulting in a quantum pressure that slowly attracts the objects.
There are two plans to turn the Casimir force into a repelling force. Researchers at St. Andrew's University believe placing a metamaterial between the objects will produce a negative refractive index, repelling the plates away from each other. The researchers admit that it likely won't happen anytime soon, but at least they're on the right path.
The second, more developed way of utilizing the Casimir effect for levitation has been under study at the University of California Riverside. By increasing the reflectivity of the objects, the quantum pressure is increased. Apparently this is the first step towards further manipulation of the Casimir effect. To wit: "Calculations show that a repulsive Casimir force could be set up between a gold-coated polystyrene sphere and a Teflon plate, if they're immersed in ethanol." Furthermore: "Although the Casimir force between any two substances-the ethanol and gold, the gold and the Teflon, or the Teflon and the ethanol-is positive, the relative strengths of attraction are different, and when you add combine them, you should see the gold sphere levitate." (sic)
Booya gravity!
No matter, we're still quite a ways from seeing people undisputedly fly. I may be buying into the Spiderman hysteria a bit, but with great power comes great responsibility, and the world in which this technology is fully developed will be a far different-and perhaps dangerous-place than it is today.
 The future will be filled with levitating wolves. Whole packs of them! ...via Flickr
Yet I can't help but feel enlightened by this technology (*self-congratulatory snicker*). One day my kids are going to be flying around to school. Goodbye morning drive!
Until then, there are a few other options. You can take up yogic hopping, which is supposedly the first step towards levitating. And I hear Yoda is giving out levitation lessons.
Resources
Wikipedia - Levitation; Psychokinesis; Yogi Pullavar; Zero-Point Energy
Youtube - How the Casimir effect works
Solreka.com - An introduction to Zero Point Energy - The fuel source of tomorrow
Life in the Fast Lane - Breaking Methods to Levitate Discovered
St. Andrews University - Quantum Levitation
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