I don't really care for "great literature" mainly because all the great literature I had to read in school was all the same. The protagonists, I can't bring myself to call them heros, made some bad decisions, gets smacked with piles of irony and them dies. Four years of that kind of story and people wonder why no one reads books any more.
That said there are a number of books that should be read because they have influenced a large number of people. These will only be a sampling but I am sure you can find some more. These are the kinds of things don't study at the beginning of your education but closer to the middle, where you are ready for some challenges to your own paradigms. For good or bad these books have inspired people and it is best to be aware of them.
Primary religious books have influenced the greatest number of people. They have inspired some people to endure great suffering and other to commit acts of unspeakable cruelty.
Economic books have had great influence on thought as well. Authors like Adam Smith, John Keynes, Ludwig von Mises, Karl Marx and Ann Rand are some of the top influencers. Right or wrong they have gotten nations to act in certain ways. It is interesting how something called the dismal science and that doesn't really try to go out and be influential, they have made some very large impacts in the lives of virtually everyone on the planet.
Those are the most influential books, then there are the much smaller inspirational books that you may have heard of, these are optional reading, because while they have been influential to many people the groups have been very small and haven't been organized to really do anything. These include works like Jonathan Livingston Seagull, Zen and the Art of Motorcycle Maintenance, The Art of War, Ender's Game, Spiritual Marketing, How to Win Friends and Influence People. You'll find a lot of these in the Self Help section of the library or bookstore.