Dune - Frank Herbert. A bit slow to start, especially if you don't have a long history of reading, but hang in there. Just a phenomenally built book. The sci-fi version of LOTR.
Shogun - James Clavell. One of the most interesting books I've ever read. Are you interested in feudal Japan? Over 1200 pages, but went pretty quickly. Not phenomenatastically historically accurate, but still fun.
Planet of Exile - Ursula K. Le Guin. Le Guin is my favorite author, though I don't agree with all of her philosophies. It's hard to say what's so great about her books, because it's often not what is there, but what isn't there. A true grandmaster. You should also check out A Wizard of Earthsea and The Left Hand of Darkness.
Neuromancer - William Gibson. If you're not familiar with this book, you will be simply astounded at its clarity of vision. Sci-fi owes much to this work.
Tigana - Guy Gavriel Kay. The best single-volume fantasy novel I've ever read. The most balanced novel I've ever read. Life, love, blood, steel, vengeance, honor, sacrifice, and your soul staring back at you with the pitiless understanding of who you are and what you have done.
Have Space Suit, Will Travel - Robert Heinlein. Again, I don't agree with Heinlein philosophically, but you can learn a lot from his books. This one has a young adult tone but is far richer than most similar works. One of the best ever written in its class.
Enemy at the Gates - William Craig. A non-fiction account of the Battle of Stalingrad, probably the largest battle in the history of mankind, and one of the most important. Thoroughly researched and humanely written. This is what war is really like.
His Needs, Her Needs - Willard Harley. Many things about love and marriage that you never even thought of. Great understanding of the dynamics of love and how to make a marriage work. The basics can be applied to any human relationship. Probably the most important book on this list, or 99.99% of book lists, for that matter.