The following should be suitable for beginning to moderate readers; the vast majority are fantasy novels.
Lloyd Alexander. The Prydain Chronicles. Begins with The Book of Three, followed by The Black Cauldron, The Castle of Llyr, Taran Wanderer, and The High King. One of the fantasy classics. Focus of the series is a young man named Taran. Fantasy.
John Bellairs, The House With a Clock in Its Walls. Bellairs wrote a great many YA books; this is (imo) the best of them. Kids who like this may also like his adult fantasy, The Face in the Frost. Fantasy.
L.M. Boston. Green Knowe series. Begins with Children of Green Knowe. A Stranger at Green Knowe is one of my favorites, featuring a Chinese refugee boy and a gorilla escaped from the London Zoo. An intriguing, calmly fantastic series set at an English estate called Green Knowe. Fantasy.
Susan Cooper, the Dark is Rising series. Great British fantasy series that uses Arthurian themes. The order of the books is: Over Sea, Under Stone; The Dark is Rising; The Greenwitch; The Grey King; and Silver on the Tree. Fantasy.
Edward Eager. Somewhat dated, but still fine fantasy series. I suggest starting with Half Magic, Knight's Castle, The Time Garden, and Magic By the Lake. Fantasy.
Elizabeth Enright, Gone Away Lake. Portia and Foster, brother and sister, are set to the country to live with their cousin Julian and his parents and discover a derelict summer community. Fantasy.
Elizabeth Goudge - A little dated but still full of flavor, Linnets and Valerians features the members of the Linnet family, four orphans who go to live with their Uncle Ambrose and his gardener Ezra and The Little White Horse, which is the story of ophaned Maria arriving at Moonacre Manor where she must end an ancient feud. Fantasy.
Brian Jacques. Starting with Redwall, Jacques has told many stories of talking mice, rabbits, foxes and assorted knightly and villainous creatures that children will enjoy. Fantasy.
Tove Jansson. The Moomimtroll series. The Moomin family lives in Moominvalley and interact with a lot of wonderful characters like the Fillyjonk, Snork, and Snufkin. Really delightful, although some occasionally dated gender stuff. Fantasy.
Norton Juster, The Phantom Tollbooth. A childhood classic that features the adventurers of Milo, who is swept away into adventurer one bored day. Fantasy.
Madeline L'Engle. The Time Quartet is made up of: A Wrinkle in Time, A Wind in the Door, A Swiftly Tilting Planet, and Many Waters. Starting with the adventurers of Meg and Charles Wallace Murray and their friend Calvin O'Keefe, the series moves on throughout the family, ending with Sandy and Dennys Murray being transported to the time of Noah. Science Fiction.
E. Nesbitt wrote around the turn of the nineteeth century about the adventurers of a family of children who discover a Psammead, or sand fairy, that grants wishes in Five Children and It. Fantasy.
Lemony Snicket. A Series of Unfortunate Events. The first book is The Bad Beginning, followed by The Reptile Room and The Wide Window. Follows the adventurers of the three Baudelaire children, 14-year-old Violet, 12-year-old Klaus, and infant Sunny. Fantasy.