This readalike is in response to a patron's book-match request. If you would like personalized reading recommendations, fill out the book-match form and a librarian will email suggested titles to you.
Sabriel by Garth Nix
Sabriel, daughter of the necromancer Abhorsen, must journey into the mysterious and magical Old Kingdom to rescue her father from the Land of the Dead.
If you liked the Abhorsen Trilogy (Sabriel, Lirael, Abhorsen), you'll also want to try (if you haven't already) some of Garth Nix's other series such as the Keys to the Kingdom and the Seventh Tower.
Also, here are a few other fantasy titles you may enjoy:

The Amulet of Samarkand: Book One of the Bartimaeus Trilogy by Jonathan Stroud
Nathaniel, a magician's apprentice, summons up the djinni Bartimaeus and instructs him to steal the Amulet of Samarkand.

Artemis Fowl by Eoin Colfer (first in a series)
When a twelve-year-old evil genius tries to restore his family fortune by capturing a fairy and demanding a ransom in gold, the fairies fight back with magic, technology, and a particularly nasty troll.

Dragonsong by Anne McCaffrey (part of a series)
Forbidden by her father to indulge in music in any way, a girl on the planet Pern runs away, taking shelter with the planet's fire lizards who, along with her music, open a new life for her.