Trying to remember what I read of my own volition/was recommended to read by my mother at that sort of age. (as opposed to books on the curriculum.)
Cat's Eye, Margaret Atwood. Not as gloomy as most of hers, has lots about 'little girl dynamics' and I loved it at about age 14.
I was obsessed with 'Perfume' by Patrick Suskind at about 15-17. Read and re-read it. Really great book, unusual topic and a page-turner.
I read my way through Gerald Durrell from about 11 or 12. My Family and Other Animals is hilarious (and the other two in that series are good too) if she's interested in animals at all. Made me want to live in Greece!
Terry Pratchett will teach her about the world.
If she's not fantasy-inclined, start her on the Watchmen books in the Discworld series. If she's likely to be interested in female empowerment (and why would she not be?!) try the Witches books, starting with Equal Rites. There's a vampire-y book or two in the canon too (is it Carpe Diem?? also The Fifth Elephant) but not his best, and also better read after she's got into the Discverse a bit. 
I always found the Hitchhikers books a bit of an acquired taste (heresy emoticon) and much prefered them on the radio - however, his Dirk Gently books are wonderful and I think I fell in love with Dirk aged about 16.
I also read 'classic' odds and sods at that age - Cold Comfort Farm is wonderful, how could anyone not like it? and Northanger Abbey (not a set book) used to make me laugh a lot. 1984, Animal Farm both pretty entertaining.
Stephen Fry's The Liar probably a bit too mature for a 15 yr old, but it's engrossing and fun.
Bill Bryson travel books are hilarious and certainly aimed at 'grown ups' but a bright 15 yr old would probably like them.
And I might be sticking my neck out here, but how about Armistead Maupin's Tales of the City books? Funny, endearing, shlocky, quick reads. They ought to be required reading, as far as I'm concerned! 