Consider for a moment the "accidents" often done by premature wizards before they are accepted into magical schools. For example, Harry's trip to the zoo with the Dursleys when he made the glass between him and the snake disappear. Or the time Harry made his Aunt Marge blow up like a balloon (actually that one Harry did in his third year. It 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? Wandless magic is merely an uncontrollable release of magic under highly stressful situations.
Wandless magic is 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, I would say that the result of a wandless spell is altogether 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 allows a witch or wizard to focus on their angry emotions whereas without one, he or she is thinking a million different things.
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/curse.
When given the chance to save herself, Lily Potter 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. It is plausible, considering her aptitude for charms, that she knew Harry would have some sort of protection from Voldemort's violence. But to suggest that Lily would not have done the same thing if she had been oblivious to this magic is a monstrous misconception. Every glimpse into her life that Jo has given us is filled with compassion.
It was that compassion which was the magical focus in this scenario. The thing that reflects - bends to - the master. The wand. 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 when he murdered her - for this love could not have reached Harry unless this horrible deed was done.
This love stayed with Harry - the proof of its presence clear in Harry and Lily's green eyes. 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 - if anything - made the connection between Harry and Voldemort stronger. It strengthened the Priori Incantatem (the bond between the wands) according to Dumbledore. It also allowed Harry to survive when faced with the Avada Kedavra spell for the second time.
Dumbledore said it best: "humans have a knack of choosing precisely those things that are worse for them." Attempting to kill Harry Potter was precisely the worst thing that Voldemort could do. In his plot to negate his own destruction by destroying the only foreseeable advisory, Voldemort started a chain reaction which resulted in his greatest fear - and the exact resolution of the prophecy he didn't want.
