I wouldn't personally choose Twilight or Hunger Games for a 10yo --but I have no objection to others' choices.
I actually own a bookstore. I guess that isn't especially important as we all have experience with kids who read... but I do encounter a lot of books and talk to a lot of people about them :)
One of my all-time favorite series for this age: Chronicles of Ancient Darkness by Michelle Paver http://www.amazon.com/Chronicles-Ancient-Darkness-Wolf-Brother/dp/0060728272/ref=sr_1_1?s=books&ie=UTF8&qid=1332985265&sr=1-1 This is the first book, "Wolf Brother". Love, love, love this series. Friends who I have recommended to have agreed enthusiastically!
I also like Sea of Trolls by Nancy Farmer. Agree with PP on The Dark is Rising. One of our kiddos actually read LOTR twice at that age.
You might consider Michael Scott's "The Alchemyst" and the sequels in The Secrets of the Immortal Nicholas Flamel series. I haven't read them yet but they are well-loved by many young folks.
My dd really enjoyed the Septimus Heap series which starts with a book called "Magyk".
I LOVE books by Tamora Pierce. She has written several short series with female heroes such as girl knights. Awesome!
The City of Ember is a good, though quick read.
And I have a huge "Warriors" series fan in the house. There are three series of six books by Erin Hunter. They are about clans of cats, fantasies based somewhat on Native American tribal life. Our youngest just started them at 9yo, she's read Percy Jackson as well so is a strong reader. They are a little "lightweight" but well-loved around here.
ETA: You might also try Half Magic by Edward Eager, it's classic, old-fashioned fantasy. Quite good. Also Chronicles of Narnia.