It goes without saying that I love JRR Tolkien, CS Lewis, and JK Rowling, so leaving that holy trinity of fantasy writers to one side, here are a few more I think are superb.
His Dark Materials trilogy (Northern Lights, The Subtle Knife, The Amber Spyglass) by Philip Pullman - An astonishing, somewhat controversial trilogy, superbly written with a level of ambition and imagination on a par with Tolkien. The story begins in a parallel Oxford, where everyone has a "daemon" (a kind of visible spirit animal which accompanies them everywhere). An adolescent girl called Lyra searches for her missing friend, which takes her to the Arctic where she encounters witches, armoured bears, and other peculiar things, whilst being pursued by agents of the "Magisterium" (a particularly nasty parallel universe version of the Catholic church). But that's just the beginning. Subsequent novels include other parallel worlds (including our world), more bizarre creatures and characters, angels, quantum physics, and more. Highly recommended. Beware the rubbish film of the first in the series (The Golden Compass is the US title for Northern Lights) which waters down much of the iconoclastic anti-religious/abuse of power themes, and cops out by excluding the very dark finale. The BBC TV series is OK though.
The Abhorsen Trilogy by Garth Nix – This clever saga is set in two fiction nations – one with technology akin to 20th Century Australia, and a second bordering land filled with magic. A tale of necromancers and sorcery, the first novel, Sabriel, features the eponymous protagonist on a quest to rescue her father from death itself. Subsequent volumes also explore the lines between the worlds of the dead and the living in interesting and vivid ways.
Artemis Fowl Series by Eoin Colfer – These surreal, thrilling and often funny adventures revolve around teenage anti-hero genius Artemis, his bodyguard Butler, and his various pseudo-villainous escapades. At the start of the series, Artemis attempts to capture and hold to ransom a rather dangerous fairy, but as the books progress, Artemis begins to work alongside the fairies against villains as diverse as the Russian Mafia, evil businessmen, insane pixies and more. Beware the rubbish recent film of the first novel.
Bartimaeus Sequence by Jonathan Stroud – Set in a parallel London filled with powerful magicians, the story begins when young apprentice Nathaniel summons the demon Bartimaeus to help take revenge on his cruel master. Notable for the witty first-person sections told from the point of view of the demon, this trilogy also has an interesting character arc for its human protagonist, who goes from pitiful yet noble to power-crazed and arrogant, and finally heroic and sacrificial.