I wrote this in my journal once:

  "Have you ever thought about what writing is? It's proof that humans cannot let go of anything. Proof that we cannot give up the chance to spread anguish to anyone we can. Well, not just anguish. But what does writing really give us? Just WORDS. Words do not fare better than real experience. Why is writing so important?
  "Had Karl Marx been illiterate, we would never have been subjected to Communism. If writing were nonexistent, we would have no Bible, no Torah, no Koran, no Kama Sutra, no Iliad, no Antigone, none of Shakespeare's plays, no Aeneid, no Declaration of Independence, no Hammerabi's Code, no Magna Carta, no Lysistrata, and certainly no spelling bees. Maybe we would be happier. If the world was uniformly educated (or uniformly uneducated, really), maybe we would be happier."

Suffice it to say, I was in a bad mood that day. But what I said was the truth; why exactly do we write? We write to express, we write to share, we write to remember. Does that make writing art?
A teacher once told me that the word "art" came from "artificial" and meant "man-made." By this definition, writing is art, and so are a lot of things. We may not consider the Erie Canal to be a work of art, but it was made by human hands and took time, planning, and talent. Not anyone can dig a canal -- just as not anyone can write a novel.
I personally believe that writing is an art, based solely on the fact that we are given an opportunity to see the world in a different way than the way it is presented through our eyes. We can see other people's views and look through their eyes just by cracking open a book or reading a sonnet or listening to a book on tape.
Art, to me, is a second-hand account of the world and how it works. Art is beauty, or the representation of life without beauty. Art is human or an image of dehumanization. Art is specific enough to apply to anything and everyone. Art can touch anyone in the world, as long as they have an open heart and allow themselves to feel.

"Art is that which the artist deems to be art."
  ~Anonymous

"Art / Is why I get up in the morning / But my definition ends there / Doesn't seem fair / That I'm living for something / I can't even define..."
  ~Ani Difranco, in "Out of Habit"

"Without freedom, no art; art lives only on the restraints it imposes on itself, and dies of all others."
-Albert Camus, Resistance, Rebellion, and Death 

 
"An artist cannot fail; it is a success to be one."