Of course, I agree with the previous posts' description of the value of reading/studying literature. I am an avid reader and cannot remember a time in my life when I wouldn't have rather read than watch TV, go to a movie, etc.
Another value of literature not previously mentioned is that good literature has the power to make a reader a better writer. Over my past 8 years of teaching high school students, I have observed that almost all of my best writers are also avid readers. While some of them prefer reading nonfiction, most of them read literature for pleasure. Their reading increases their vocabularies and provides a wide variety of writing styles which they model (often unconsciously) in their own writing.
Literature is a wonderful way to learn, to enjoy, to escape, and "see the world," all from the vantage point of a reading chair. It's possible in the U.S. to read pretty much any book you want for free, with the public library system we have.
Literature gives us a way to identify with others. Timeless, classic themes are such for a reason: they appeal to the human spirit.
Literature is the recording of the human heart, the human experience; it is the true history book, the true cultural recording. If one reads a Russian novel, does one not learn about the Russian people? the Russian psyche?
Emily Dickinson wrote that "There is no frigate like a book/To take us lands away"; certainly, the reader can travel in history by returning to another age, or by entering the culture of another country. The value of literature? What, indeed, is the value of learning about others? Does it not make us richer for the experience? ask996 is absolutely right: "We must establish the value of literature for ourselves."
I don't remember who said this, but the quote went something like this, "It's not a matter of how many good books you can get into; it's how many good books can get into you." That being said, what constitutes valuable literature is subjective.
Valuable literature should offer something to the reader in terms of hope, encouragement, escape, empathy, love, knowledge of human nature, relationships, and etc. So undoubtedly the message someone gets from one piece of literature will be different than what someone else gets. Perhaps this means that for each of us, we must establish the value of the literature for ourselves.
Through literature we can see into other people's lives and become more understanding or tolerant. Everytime I read a novel or a poem expressing a new way of seeing something, I feel like I've grown. For example, when I read the book Mountains Beyond Mountains: The Quest of Dr. Paul Farmer, I learned about history in the poorest areas of Haiti. I also learned abut the life of a dedicated doctor and why he would choose not to pursue a lucrative career in Boston, but instead work to help the poor people of Haiti. After I read the book, I felt as though I had gone to Haiti myself.
I think that the value of great literature is that it transports us to another place, through another pair of eyes and we learn about the hearts and minds of other people, as a result.
There will be many answers to this question. In my mind, the value of literature is any work which can significantly enhance the questions put forth by Leo Tolstoy: What can we do and how shall we live? I believe that these particular questions help to frame the usefulness of literature. Any work which considers to be literature has to address both questions. Literature, in my mind, makes itself to be a work that allows a sense of light to these particular questions. I think that when we can examine how literature seeks to broaden the scope of these questions, one can understand works in their place of the pantheon of literature.
The value of any great work is in the theme that it leaves in the mind of the person who appreciates it, and if that theme can be true when it was written to the present, that work deserves to be called literature. It has to have a timeliness to it.