Thank you, everybody, for the suggestions. We have a lot of these films already (I have a compulsively large movie collection) but there were a lot we didn’t have. I’ll talk it over with Mrs. R.
However, Mrs. R has suggested an iPod, which might use up all our money 
You can buy an iPod look-alike for quite a bit less. And you can get one with less memory that will still service the needs of a 15-year old. My husband got me a Lyra (by RCA) and I’m pretty happy with it. It holds 8 hours of music and I think he only paid a little over $100 for it.
Zero Effect. It’s a great modern-day detective movie.
How about “Gregory’s Girl”? A Scottish teen flick from the 80’s.
Ghost World is a great movie for teenage girls (if not a little depressing). There’s no pygmalion transformation, big prom or unattainable hot boy.
How about 13 Going on 30?
The NoteBook,
saddest movie ever, my students recomended this to me, the perfect chick flick in many ways and it has Rockford, er James Garner in it.
Bend It Like Beckham is a must-see film, both for girls her age and everyone else as well.
The films I enjoyed when I was 15ish (I’m 23 now, so it wasn’t a long time).
Anything by Bruce Lee (for the muscles, not the violence, obviously), Fists of Fury * or Enter the Dragon by preference.
*
Breakfast at Tiffany’s
North by Northwest
Vertigo
Psycho
The Birds
Dazed and Confused
Empire Records
Reality Bites
Clueless
Legends of the Fall
Dirty Dancing
Leon
My Own Private Idaho (for Depp and Phoenix, obviously)
These were all movies that my friends and I would watch over and over again, to the point where we knew all the lines and could dissect everything in great detail, all while lusting after the main character and eating vats of popcorn.
Films I would have watched if they had been out:
Garden State
Coming Soon
Mean Girls
Films my 17 year-old sister has enjoyed recently:
Y Tu Mama Tambien
Le Choriste
The Pianist
The Notebook
The 40-year old Virgin
Zoolander
Bad Santa
Obviously all of these, with the possible exception of *Le Choriste, Mean Girls * and The Notebook, will have tipped the sex, language and violence scales. You know your daughter best, but if you think she could handle films with a more adult theme, then go for it.
I should say that we watched those movies sometimes with parental permission and sometimes not, but that none of us are worse people for it.
When we were 16, my school would show *JFK * and Schindler’s List for history class and All About My Mother in Spanish class, so you can see that our definition of age-appropriate cinema might be very different.