I will echo anything by Madeleine L'Engle - her Austin Family Chronicles are just as good as the Time Quartet without being as overtly fantastical. If you can find a copy, I'd also HIGHLY recommend
The Other Side of the Sun as well. Found that one in college and just fell in passionate love with Madeleine's language.
Diane Duane is a little more forthright version of L'Engle - in fact, I heard an interview of hers where she said L'Engle's novels frustrated her because they never answered the big questions. To me, that was the whole point, to get kids thinking about the big questions without answering them for them. But I love both authors dearly, and their writings really do complement each other.
To me, Duane and L'Engle kind of make most other YA fantasy seem rather weak in comparison. However, I think that's my adult reader perspective "tainting the sample" so to speak. A lot of the stuff out there is completely inoffensive and lots of fun.
Francis Hodgson Burnett is a definite winner - though be warned, once you read
A Little Princess it will ruin every movie version you've ever seen (or at least every one I've ever seen - there might be one out there that does it right).
One I'll add that I haven't seen anyone mention yet is Cynthia Voigt. I read
Jackaroo and its sequels as a teenager, then moved on to The Tillerman Cycle starting with
Homecoming and
Dicey's Song. Very worthwhile.
The Indian in the Cupboard series is another good fantasy romp - I read those much later than 13 and thoroughly enjoyed them. In fact, most of what I'm listing here I read in my late teens or later. I have a minor passion for youth literature - it's always ABOUT something, as opposed to so much of grown-up fiction, which is just about entertainment.
Another nifty fantasy suggestion would be Robin McKinley -
Beauty in particular. Though some of her stuff (right now I'm thinking of
Sunshine) would be much older than I'd want a 13-year-old of my influence to be reading.
If you can find any copies, Sylvia Engdahl has several young adult sci-fi novels that are really great, though they're from the 70s. You can tell Engdahl was heavily influenced by the sci-fi ideals of the era, i.e.: once we get into space, humanity will finally unite in a common purpose - huzzah!
Enchantress from the Stars and
The Far Side of Evil are the two I found while I was still in school that I absolutely fell in love with and checked out of the library over and over until the library eventually lost or retired their copies. The books were recently reprinted in GORGEOUS hardcovers, but those were typical hardcover prices. I still run across used paperbacks once in a while - in fact I have a couple to read from in order to keep my hardcovers pristine.
Oooh, the Myst books (based on the computer game) are really good too, and very age-appropriate without being dumbed down. They have a great "neverending story-ish" feel of being able to jump into the story. You might have to find them used though - if they're not out of print, I'd be surprised.
One more non-genre suggestion - the Anne of Green Gables books. Might even start her off with the PBS series to whet her appetite. There's nothing gets a teenage girl's interest like a crush on Gilbert Blythe!

(Unless maybe a crush on Austen's Mister Darcy - probably should throw
Pride and Prejudice into the mix as well.

Oh and
Jane Eyre while your at it - let her stew over whether Mister Darcy or Mister Rochester is hotter.

)
Please steer her clear of Twilight and its ilk if at all possible. There's a lot of dark, paranormal (and non-paranormal) romance crap out there right now being marketed at young girls, most of which I would venture to say is very unhealthy for them to spend all their time feeding their minds with. The vast majority of what's mentioned in this thread is literature with characters that will challenge and inspire a young woman. Good luck! Frankly, I'm jealous. I don't have a young girl to share all my wonderful literary discoveries with.