Imagine being able to levitate that pen (or quill) your dropped or never having to worry about losing your wallet again, because you could just summon it with a flick your wrist.
This is why wands are indispensable in the Harry Potter universe. Your wand is basically an extension of you that conjures spells in a world where things like TV and the internet don't exist except as curious topics of study for the Misuse of Muggle Artifacts department in the Ministry of Magic. How else would you be able to unlock forbidden doors, light your way in the shadows, fight off Dementors, disarm an entire squad of Death Eaters, and stun enough of them to avoid getting slammed by Avada Kedavra?
You couldn't possibly pass your O.W.L.s unless you're fluent in certain spells. What kind of wizard or witch doesn't light up their wand to read in the dark or float inanimate objects into their hands? Walking over and picking up your glass of pumpkin juice is such a Muggle thing to do when you can levitate it.
There is no such thing as a Lost and Found in Hogwarts, because students can just summon whatever they've lost, unless you're Luna Lovegood and firmly believe Nargles got away with your shoes.
The only exception to this is the Patronus charm, because that is far beyond even N.E.W.T. level… if you can ignore the fact that half the teenage corps of Dumbledore's Army are able to conjure the elusive corporeal Patronus.
While many more spells are necessary for survival in a world where you never know who is hiding the Dark Mark up their sleeve and He Who Shall Not Be Named has revived himself by drinking unicorn blood and snake venom, you wouldn't even have a chance at firing a counterspell without having these in your arsenal.
To celebrate the Harry Potter films making their way to SYFY (debuting on July 13), consider this your crash course in witchcraft and wizardry with our view of the 7 Essential Harry Potter universe spells.