Harry wears glasses. They were frequently broken by Dudley over the years before Harry shipped off the Hogwarts for the first time, and they are wrapped with tape. After his glasses were damaged by his first trip by Floo Powder, Arthur Weasley repaired them for him with a silent Mending Charm (CS4).
Percy uses a Mending charm to repair his own broken glasses (GF8). Other characters who wear glasses include Dumbledore, Myrtle Warren, Sybill Trelawney, and Professor McGonagall.
Rowling comments on Harry's glasses:
I was wondering why Harry had glasses?
JK Rowling: Because I had glasses all through my childhood and I was sick and tired of the person in the books who wore the glasses was always the brainy one and it really irritated me and I wanted to read about a hero wearing glasses.
It also has a symbolic function, Harry is the eyes on to the books in the sense that it is always Harry's point of view, so there was also that, you know, facet of him wearing glasses.
Some fans have noticed that in the films, Harry is the only student in Hogwarts with glasses. This is not the way Rowling envisions things, however, as evidenced by this comment:
In the second book, if you see a basilisk and you are wearing glasses, will they protect you? And if they do, why did Moaning Myrtle die, and if they don't, why not?
JK Rowling: That is a really good question. And I have been asked that before. I had to decide the glasses couldn't protect you. I just had to, because obviously there would be quite a few people at Hogwarts who were wearing glasses and I thought that might cause me plot difficulties, so I decided that glasses alone wouldn't protect you.
But as you know, I had Justin protected by the camera lens, so I think I am open for criticism there, but the way I explained to myself he was looking through several lenses and wasn't actually seeing the thing directly, it wasn't through his eyeline, when you look through a camera you are looking through the lens, it is a little distorted. You can argue with me on that and I wouldn't blame you but that is how I explained it to my self at the time.