When most people think of fantasy fiction they imagine knights and maidens, maybe a dragon or other fantastical creature, possibly wizards and magic. While all or some of these elements may be present, the fantasy genre entails a wide variety of possiblilities. The following are a few sub-genres, but often novels may have elements of more than one type.

High Fantasy tales often have a serious tone, with events on an epic scale and usually takes place in a psuedo-medieval setting. A common theme in these novels is the fight against evil and characters many times have a quest they must complete. Often they include fantastical races or creatures. Examples of high fantasy include:
The Lord Of The Rings trilogy by JRR Tolkien
Sword of Shannara series by Terry Brooks
Wheel of Time series by Robert Jordan
Earthsea trilogy by Ursula K LeGuin
A Song of Fire and Ice series by George RR Martin

Sword & Sorcery tales have plenty of action along the lines of classic epics like The Odyssey and The Iliad. Examples of sword & sorcery include:
The Conan series

Contemporary Fantasy (also called Urban or Modern Fantasy) takes place in the modern world. Travel to alternate worlds may be possible, or the existence of hidden magic. Examples of contemporary fantasy include:
The Harry Potter series by JK Rowling
Abarat by Clive Barker
Here, There and Everywhere by Chris Robeson

Dark Fantasy is closely related to and often includes elements of the horror genre. The supernatural, or supernatural creatures, such as vampires, are often a main ingredient. Many times, these novels are officially labeled either fantasy or horror, depending on which genre they lean more towards. Examples of dark fantasy include:
The work of HP Lovecraft
The Work of Neil Gaiman
The Elric stories by Michael Moorcock
Stagestruck Vampires by Suzy Charnas McKee

Historical Fantasy incorporates a fantasy storyline into history or invents a fantasy history that mirrors our own. Some example of historical fantasy include:
The Crown Rose by Fiona Avery
Jonathan Strange & Mr Norell by Susanna Clarke

Fairytale Fantasy encompasses many diverse works.both modern fairytales and reworking of classic stories. They may be aimed at children, or contain more adult themes and content. Also closely related is Mythic Fantasy, which draws on mythology. Some examples of fairytale fantasy include:
The Sword of the Rightful King by Jane Yolen
The Fairy Godmother by Mercedes Lackey

Comic Fantasy fiction satires the conventions of the fantasy genre and sometimes non-genre work. Examples of comic fantasy include:
A Hat Full of Sky by Terry Pratchett
Xanth series by Piers Anthony