I've actually used the Harry Potter wand system as one of the inspirations for the hybrid Wizard/Cleric class in my homebrew.
trav_laney said:
Wandless Magic: in rare instances of the book, magic is done without the benefit of a wand (when Harry makes the glass disappear in the snake terrarium, or when Professor Quirrell surrounds the room with fire). And according to J.K. Rowling herself, "You can do unfocused and uncontrolled magic without a wand (for instance when Harry blows up Aunt Marge) but to do really good spells, yes, you need a wand."
Alternate Interpretation #1:
Cantrips don't require a wand at all. This is one I used for our system, although with a Feat we allowed the Wizard to do the same for his "Domain" spells. Most of the things Harry did without a wand could be explained through use of Mage Hand, Light, etc. A "disarmed" wizard wouldn't be completely helpless, but close to it.
Alternate Interpretation #2:
Wands are a substitute for Material Components, and vice versa. We also use this one.
After all, the books contain quite a few examples of non-wand magic: Potions, the Centaurs' prophecies, etc. Effectively, Wands and Component Pouches could fill the same niche; it's much easier to have to keep track of a single focus item, but it's not a necessity.
This also explains all the material components seen in the books. If you're working in a medical ward, it's much easier to keep the three or four common materials used for healing spells on hand than to keep pulling out your wand. Also remember that they're at a school; at home, few wizards would have materials for anything other than the most commonly-used spells (floo powder?), and so would rely on their wands for everything, but at a place like Hogwart's, they'd have all sorts of rare materials on hand.
Alternate Interpretation #3:
Without a Wand, a Wizard must make a Spellcraft roll to see if he gets the effect he wanted out of the spell, with the DC scaling with spell level. In the books, we don't normally see the high-level wizards trying to cast "low-level" spells, so we don't know if wands are strictly necessary for those.
Alternate Interpretation #4:
A Wizard can expend something to cast spells without a Wand. You could have it cost HP, which'd explain why it doesn't get done often. Or, you could take a page from the Psionics rules and have it expend the equivalent of "Psionic Focus", which is why it only happened when Harry got angry, and why he didn't do it repeatedly.
But as others have said, we've seen a single type of magic, from a single school, whose students come from a small geographical area. It could just be an affectation among one small sample of wizards.