The Last Man on Earth Clubwas pretty good.
The Greatwinter trilogy starting with Souls in the Great Machineis worth a look.
Gah, I came in to say 1984 and Hunger Games; should’ve guessed my fellow Dopers would beat me to it.
Um, how about 11/22/63?
How about some Vernor Vinge? Fire Upon the Deep/Deepness in the sky are good strong SF stories with dystopian elements (eg “the Emergency”) but ultimately quite optimistic - and one of the chief heros of AFUtD is a fourteen year old girl. The Peace War/Marooned in Realtime are post-apocalyptic trying-to-get-society-back-on-track books (Marooned in Realtime is a post-post-Apocalyptic detective story, and you don’t see many of them about ) Light on the sex and violence, but pretty philosophically deep.
If you don’t mind going “dated” again (well, I don’t find his writing dated, but 60s mores do pop up now and again. Of course, if you don’t want to go overboard on sex and violence, there’s plusses to that…), John Brunner pretty much owns “dystopian SF” and if she did get into his books you wouldn’t have to worry about new reading matter for about a year 
- I’d suggest* Polymath (Castaway’s World)* and* The Infinitive of Go* as testers.
Oh hell yeah. The Sparrow left me an emotional wreck, and I was about thirty when I read it. It’s awful. I mean, wonderful. But awful.
I’ll tack on some John Christopher - YA, and perfectly acceptable for young folks, but still decent. There’s the Tripods trilogy, of course: The White Mountains, The City of Gold and Lead, and The Pool of Fire, but I like the Sword of the Spirits trilogy better. That’s The Prince In Waiting, Beyond the Burning Lands, and The Sword of the Spirits. Still suitable for teens, but with a harder edge to it. The protagonist has flaws - lots of them. Only way it may not be suitable is that these are very “boy” - centered books.
Aurora by Kim Stanley Robinson.
It’s SF, not exactly dystopian but not entirely a happy ending either. More bittersweet. Female protagonist. Beautifully written.
Add my support to Octavia Butler. Beautiful writing and ideas.
How about Snow Crash? Jeez it’s a classic by now :(. IIRC, the girl YT is pretty much a good female lead.
Stranger in a Strange Land isn’t a dystopia, and Do Androids Dream of Electric Sheep is a pretty weak book–a rare case where the movie is 37,923 percent better than the book.
(eta: and any parent that would subject their child to anything by Ayn Rand doesn’t deserve to be a parent.)
There’s probably some Heinlein that would work, but agreed that Stranger isn’t it. Problem is, I don’t know of anything that I’d suggest to a non-Heinlein reader that’s also somewhat dystopian. Maybe Job. Otherwise give her the juveniles and collections of short fiction if just sci-fi is enough.
And yes, I think some Dick could be in the reading pile, but I agree that probably not Do Androids Dream of Electric Sheep. Again, the problem is I’m not sure what novels to really suggest. I’d think more along the lines of a good anthology of his short work–there’s a reason most of the movies based on Dick’s writing is his short stories and novellas.
It’s surprisingly hard to come up with additional good dystopias. At least in the classic sense. More apocalyptic/post-apocalyptic is easier. Lots of writers have done some of that. In the really somewhat silly vein is John Ringo with his Council Wars and Black Tide Rising series.
How about Earth Abides?
Tell us about 1984 vs Brave New World if she makes it through both. My gut instinct, having read both those books at about that age (but as a boy), is that Brave New World will be liked somewhat better and will be considered far less of a slog than 1984.
Well, there’s the City of Ember series, by Jeanne DuPrau, which she may have encountered already and might be a little young for her.
There’s the Matched trilogy. I lost interest halfway through the second book, but that may have been because they’re very teen-girlish.
Another possibility is the Forest of Hands and Teeth series, which is very zombie-apocalypseish.
For something somewhat more grounded, there’s the **Life As We Knew It** series. An asteroid hits the moon, throwing it into a different orbit and causing global chaos.
Another more realistic one: the seven-book Tomorrow series, starting with Tomorrow, When The War Began. The female protagonist is an Australian high school student. She and her friends go camping deep into the Australian wilderness, but when they return, Australia has been overrun and conquered by a nameless nearby nation. Do they give themselves up, hide, or fight?
One sci-fi series that might be a possibility is the Lorien Legacies, starting with I Am Number Four. The gist: when their home planet is invaded, nine children from the world’s elite Garde are sent to Earth with protectors so that they can mature and return. They are Charmed in a way that they cannot be killed but in a specific order. The first three are dead, and the book follows Number Four.
And finally, a series I cannot recommend highly enough: Chaos Walking, which starts with The Knife of Never Letting Go. Seriously awesome. Todd is growing up on a world infected by the Noise germ, which killed all the women and causes everyone’s thoughts to constantly be broadcast to everyone nearby. Todd and his dog make to escape their town, but they stumble upon something strange: a patch of silence, with a girl at the middle. The story is very gritty, and takes surprising twists and turns.
Has anybody here read Sinclair Lewis’s It Can’t Happen Here? Is it worth a read?
Earth Abides is a good choice.
I suggest Alas, Babylon. It might be a little dated - aftermath of a nuclear war - but it’s definitely a good read.
As a 14 year old girl interested in sci-fi, I read and enjoyed
David Brin (Earth, especially – basically predicted the internet)
Jonathan Barnes (some sexual content)
Neuromancer
Heinlein’s Moon is a Harsh Mistress
I did not care for
*Stranger in a Strange Land
Brave New World
*Kim Stanley Robinson
Take that for what you will…
A 14-year-old should not have any trouble reading adult literature. Any book is well within her grasp. You are not doing her a favor by limiting her exposure to Young Reader titles, or books that adults think are “easy”. If it’s a well-received book in the genre with good general reviews, she will read it and enjoy it.
I would tend to agree, but realize that, realistically, someone who chooses a username that spells out “gospel” might possibly be a bit more conservative about such things.
She might like Babel-17.
I’m mobile, so can’t/won’t provide a lengthy defense of my choice, but I nominate Hugh Howey’s Silo series.
Cause mobile, also can’t make pretty link
How about Unwind, Unstrung, and Unwholly by Neal Shusterman. I know a couple of years ago it was very popular with the young teen crowd.
I recently read and enjoyed The Girl With All The Gifts
StG
Hmmm. I see movie of that On Demand. I’ll have to take a look.