It always bothered me that they needed the wands to do magic. In the first film/book, before Harry went to Hogwarts, there were instances of him using magic unintentionally without the use of a wand (such as turning his teacher's wig blue).
Why do they need them? Are there any that don't need them to intentionally use magic, if so, why?
Clarification edit: I mean are there any that are able to do magic well without the use of a wand?
I would imagine that European wizards like Harry who are used to always having a wand when performing magic, would find it difficult to do so otherwise. However, in some other of the globe, wands are rarely, if ever, used.
The wand is a European invention, and while African witches and wizards have adopted it as a useful tool in the last century, many spells are cast simply by pointing the finger or through hand gestures.
(Pottermore - Uagadou)
The magic wand originated in Europe. Wands channel magic so as to make its effects both more precise and more powerful, although it is generally held to be a mark of the very greatest witches and wizards that they have also been able to produce wandless magic of a very high quality. As the Native American Animagi and potion-makers demonstrated, wandless magic can attain great complexity, but Charms and Transfiguration are very difficult without one.
(Pottermore - History of Magic in North America)
The examples of Harry doing the wandless magic with the snake and blowing up his aunt are actually good ways to explain why wizards, specifically young ones at Hogwarts, use their wands. The wandless magic Harry uses is sloppy, unpredictable, and mostly unintentional. Harry can't do wandless magic "on command". Only powerful and fully trained wizards, Dumbledore for example, can do wandless magic. The wizards use the wands and the spell words to direct their magical energy into an intentional and predictable action. If you'd like, the wands are like training wheels. Plus, wandless magic probably requires a lot of energy and tires the wizard faster than if he/she had help channeling their magical energy.
(Related to the question: Harry only does wandless magic when he is angry with someone, much like how Tom Riddle made "bad things happen" to people who were mean to him. This is an ability which, like parseltongue, was 'given' to Harry with Voldemort's soul, so he wouldn't necessarily be able to perform it if he were not the Chosen One.)
For more information, check out the Harry Potter Wiki page on wandless spells, which backs up the points I made.
They don't need the wand to perform magic, as you say and as evidenced throughout the books. However, the wand is an instrument that's used to channel magic - I'm pretty sure this is explained somewhere in the books but I don't recall exactly where to try to grab a quote - so while it's possible to intentionally cast (at least some) spells without a wand, it's much easier to do so using a wand. That's particularly important for young wizards who are still learning how to control their magic.
There are some spells that seem to absolutely require a wand. Lumos appears to function by focusing magic through the wand's core to produce light, and some spells mentioned in the books (such as the Levitation charm Leviosa) seem to require a very specific wand movement to work correctly.
Just to add to the above answers, the core feature of a wand is the Magical element from a magical being that is within it i.e. a Phoenix feather or a Dragon heartstring. As answered above the wand simply channelizes the Magical energy of the Wizard/Witch to focus it to do conscious and powerful spells. Even is seen to be doing wandless magic when trying to save Harry when he is on the bewitched broom during a Quidditch match.
think of it like an AM/FM, the signals (radio or magical) are there, but without the right equipment (receiver/wizard or witch) they are not realized and without the antenna (wand) they can't be used effectively.
