The Sorting Hat
Students are Hogwarts get sorted into one of four houses by the Sorting Hat. Why? Because it's tradition. Don't question the magic, just enjoy it.
Last year, if you'll remember, the Sorting Hat contemplated putting Harry Potter in either Gryffindor or Slytherin. He wound up in Gryffindor because that's where he asked to go. This year, Harry's wondering about that a little:
SORTING HAT: Bee in your bonnet, Potter?
HARRY POTTER: I was just wondering if you put me in the right house.
SORTING HAT: Yes. You were particularly difficult to place. But I stand by what I said last year. You would have done well in Slytherin.
HARRY POTTER: You're wrong.
Dang. That was not the news Harry wanted to here. Is he really even a Gryffindor? Could he be the heir of Slytherin? Does the Sorting Hat make mistakes? It is just a hat after all.
Harry is a little bit reassured when Fawkes brings the Sorting Hat down into the Chamber of Secrets and he's able to pull the sword of Gryffindor out of it to slay the basilisk. As Dumbledore tells Harry, "It would take a true Gryffindor to pull that out of the hat." Quite right.
In some ways, you could say the Sorting Hat decides the destiny of each student, but that's not exactly right. Harry had qualities that would have made him suitable for two different houses, but he chose to be in Gryffindor. The hat didn't decide. Harry did. So maybe the Sorting Hat doesn't choose for the students. It just helps them make sense of their own choices.
That's one impressive hat.