If you like Dragonquest by Anne McCaffrey

If you enjoyed DragonQuest, here are some other titles you may like:

Dragonflight by Anne McCaffrey. (Dragonriders of Pern no. 1)
HOW CAN ONE GIRL SAVE AN ENTIRE WORLD? To the nobles who live in Benden Weyr, Lessa is nothing but a ragged kitchen girl. For most of her life she has survived by serving those who betrayed her father and took over his lands. Now the time has come for Lessa to shed her disguise--and take back her stolen birthright. But everything changes when she meets a queen dragon. The bond they share will be deep and last forever. It will protect them when, for the first time in centuries, Lessa's world is threatened by Thread, an evil substance that falls like rain and destroys everything it touches. Dragons and their Riders once protected the planet from Thread, but there are very few of them left these days.
Now brave Lessa must risk her life, and the life of her beloved dragon, to save her beautiful world. . . . "From the Paperback edition."

The Fellowship of the Ring by J.R.R. Tolkien. (and the sequels)
In a sleepy village in the Shire, young Frodo Baggins is faced with an immense task as his elderly cousin Bilbo entrusts the One Ring of Sauron to his care. Frodo must make a perilous journey across Middle-earth to the Crack of Doom, there to destroy the all-powerful Ring and foil the Dark Lord in his evil purpose.

Sabriel by Garth Nix. (and the sequels)
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.