Consider, for a moment, the "accidents" often done by premature wizards before they are accepted into magical schools. Take for example Harry's trip to the zoo with the Dursleys when he made the glass between himself and the boa disappear. Or the time Harry made his Aunt Marge blow up like a balloon (actually that one Harry did in his third year, but he was under high-stress). These events proved random explosions of magic may exist in a witch or wizard despite relative magical control.
But that's exactly my point, isn't it? These spontaneous eruptions of magic in youth are examples of wandless magic.
It would follow, then, that wandless magic is primarily hard to cast because it is driven by emotion. Considering the range of emotions a human can hold, a spell meant for sparring could potentially kill someone.
Yes, because of its nature to act wildly, a wandless spell has the potential to be far more powerful than that of a spell done with a wand. And yet, unforgivable curses cannot be cast without one. Why? As we know of unforgiving curses, you have to "mean them." Perhaps a wand not only provides a physical focus but a mental one as well, giving witches and wizards conscious control over their own influx of magic. Certainly a helpful tool, in the hands of an irrational killer.
Proof of the real danger of wandless magic may be revealed in the life of Ariana Dumbledore. A girl gifted with extraordinary magical prowess, Ariana's temper was explosive - literally - and it was one of these explosions that killed her mother, Kendra.
There has been one significant application of wandless magic in the Harry Potter books, and it set the foundation for the entire plot ten years before Harry was accepted into Hogwarts: Lily Potter's love.
When given the chance to save herself, Lily adamantly put herself between Voldemort and Harry and continuously pleaded, "Not Harry, please no, take me, kill me instead." Blinded by this human devotion that he had never understood, Voldemort fiercely slew Lily - unknowingly triggering a very "old" magic.
Indeed, in an ultimate act of love, Lily sacrificed herself to save Harry. We might wonder if, considering her aptitude for charms, Lily knew Harry would have some sort of protection from Voldemort's violence after she sacrificed herself. If she was aware, than she succeeded at consciously generating the wonders of wandless magic - an incredible feat considering the place where that magic pulls from.
Without a wand, compassion was the magical focus in this scene. On this occasion, Lily's maternal instinct was strong and her emotions were singular. It was not only Lily who activated this bit of wandless magic. Voldemort played a key role by providing the proper situation for Lily's magic to take effect.
The spell was so powerfull it stayed with Harry through all seven books, and presumably beyond. But this special protection did not diminish when Quirrel attacked in the first book, nor when Voldemort took Harry's own blood to build his body. The latter - in fact - made the connection between Harry and Voldemort stronger. It strengthened the Priori Incantatem between the wands according to Dumbledore. It also allowed Harry to survive when faced with the Avada Kedavra spell for the second time.
We tried to shut him in a pyramid, but Mum spotted us.
George Weasley Prisoner of Azkaban, Chapter 4, Page 63
When Arthur Weasley takes Harry and his pals to the Ministry of Magic they must first dial a secret code into a telephone keypad. He enters the number 62442. The letters underneath those numbers on a standard mobile phone spell out the word "magic".