Tolkien said that some of the purposes of fantasy are to satisfy certain primordial human desires, among which are the desire to survey the depths of space and time and to hold communion with other living things. 

Also in "On Fairy Stories" he discusses the desire for recovery, escape, and consolation.

            recovery is the ability to see familiar things in a new light

Tolkien was especially interested in nature, for he said "Faerie contains many things besides elves and fays, and besides dwarfs, witches, trolls, giants, or dragons: it holds the seas, the sun, the moon, the sky; and the earth, and all things that are in it: tree and bird, water and stone, wine and bread, and ourselves, mortal men, when we are enchanted."

escape does not make the "real world" less real, but allows us to better explore it by seeing alternatives.  We understand the rules of our own Primary World by exploring a Secondary World with its own self- consistent rules.  Or as Ursula LeGuin says, "It is a different approach to reality, an alternative technique for apprehending and coping with existence."  She also calls fantasy "a distancing from the ordinary."

consolation Tolkien would call the promise of a happy ending, those his are hardly sorely joyful.  His eucatastrophe is more "a sudden and miraculous grace," an echo of Christ's rising again on the third day to conquer death.

Often the making or testing of a hero, using Campbell's stages, which include, but are not limited to the initial testing which the hero fails, the learning phase which often involves an older, wiser, Wizard-like mentor and as often requires a quest or journey with a specific object at its end, and during which the hero must often go underground (or in the extreme case into Hell itself), and often pass through water in a kind of baptism, before being tested again and winning the prize.  The journey can be epic in scope, that is affecting a whole community, but it need not be so large.  Le Guin says "Fantasy is a journey.  It is a journey into the subconscious mind."  It can be a coming of age story or mythic or epic in its scope.

Throughout there may be magical talisman or objects, talking birds or animals, and unlooked for friends and enemies along the way.

The setting is often Medieval looking.  At any rate there is a sense that the Golden Age is in the Past, before the time period of the story, and that the world is declining from such splendor.  There is no technology and weaponry is generally simply with nothing more recent than cannon and more often limited to bows and swords.

Power comes not from mechanical devices or technology but sometimes from magic, often derived from nature or language.  The spoken word, chant, incantation, spell or song can have power.  But often the characteristics the hero needs to be successful are not connected to the magical talisman (a Ring, etc.) but come from within: perseverance, knowledge, compassion.

The language of Fantasy need not be different from that of mainstream fiction, though it can look archaic.  However, just a sprinkling of "thee's" and "anon's" does not make a work fantasy. Le Guin states that fantasy heroes have a "greatness of soul [which] shows when a man speaks."  It is generally figurative and evocative language.  The stories are generally of a serious nature, at least a serious theme, but that does not exclude humor.

Much of my definition speaks more to "High Fantasy" which excludes ghost stories, animal fables, folk tales, or satire, though those can be considered Fantasy also.

Another common theme which is represented in much of 20th Century fiction, not just Fantasy or Science Fiction is a concern with the creative process, how stories are invented/discovered/ written.