I would recommend True Grit for a teen girl. It is the reminiscence of an stubborn old lady recalling when she was a young girl trying to enact revenge on her father's murderer. The voice of Maddy Ross is crotchety and biased and no-nonsense. Definitely a book that my two year old daughter will read one day.
If a teen girl is looking for something to read I would first suggest series that have proven popular with their generation, like Harry Potter or the Hunger Games. Not everyone will be interested in the same thing though, so if fantasy is not their thing then have them explore different genres until they find something they like. There is also no shame in reading a book below your reading level! Find some humorous books for children like Junie B Jones that can be read in just an hour or two. Any reading is good reading!
A number of excellent authors are available for enjoyment by teen girls. These books are interesting but free of the unnecessary profanity and violence that pervades some literature today. Many girls enjoy the Twilight series, while others still enjoy the Harry Potter Series. Madeleine L'Engle also wrote several excellent fictional novels.
I try not to read books that are strictly "gender coded" , because I don't like the segregation and the whole "you can't read this book because it's for BOYS" thing. However, I have read some books that I think a girl would enjoy.
Ask the Passengers - A.S King. (If you don't like homosexuals however, don't read it.)
Please Ignore Vera Cruz - A.S King
Unicorns VS. Zombies - Holly Black
The White Cat - Holly Black
Impulse - Ellen Hopkins
Anne Dressed in Blood - (an author I can't recall)
Au Revoir Crazy European Chick - By a really cool guy I can't remember!
The Enemy series - Charlie Higson
Hunger games. Decent reading. Somewhat sci-fi. Pretty good and decently written.
Twilight. For girls not smart enough to read the hunger games
Game of thrones (book). Read it. Read it now!
Graceling. Pretty good. Female character perspective.
Witch and Wizard. Pretty good. Written a lot like Kane chronicles (Rick Riordan. I don't recommend anything by him.) Decent plot, but a little sad.
Maximum Ride. I didn't like it, but you might.
This will be fun!!! So, I have read many books in my 15 years, all of them great. Let's see, there is the Hush Hush series, slightly inappropriate for kids, who are like 10, but ok for a teenager no sex in it, but some awkward stuff, in my opinion, and slight violence. There is Going Vintage, it just came out this year, but i was awake until like 3 in the morning once, just so i could finish it, but the ending kind of frustrated me, those with easy anger and uncontrollable fangirlism should probably not read this. Lastly, Spoiled. It was terrific, but i didn't like how the point of views kind of changed, while the context was still in the 3rd person, it was extremely confusing, people who do not like soap operas, i do not recommend this to you, since it is in the same format i have just explained. Happy reading :)