As long as you avoid anything written by Ayn Rand and Ernest Hemmingway, you should be OK.
I would recommend that you read "One Flew Over the Cuckoo's Nest" by Ken Kesey, and then watch the movie with Jack Nicholson because they both kickass (even though the author dissaproved of it)
Another good book is Exodus by Leon Yuris, but the content of the book might be too Zionist for some people's tastes.
If you're looking for a fantasy book, the Hobbit by J. R. Tolkein is an all time classic, though I haven't personally read it.
If you're looking for an action novel (and have lots of free time on your hands), Shogun by James Clavell is quite good.
If you're looking for a sci-fi novel that's different from the usual formulaic Michael Crichton crap-o-rama, I would recommend "Ender's Game" by Orson Scott Card. The book was written back in the 1970's, but it's remarkable how farsighted it is.
If all you want is a timeless American classic, few have been dissapointed with Mark Twain's "Huckleberry Finn". I would avoid "The Adventures of Tom Sawyer" though, as it's more of a kiddy book.
I'm looking for good reading, mostly classics like "Catcher in the Rye" for example, or "Walden" by Thoreau. Stuff like that, to enhance my thinking. But I am very open to sci-fi as well, or fantasy.
Though there are several thousands of books known as "Classics", I can recommend about a dozen that you should read:
The Odyssey by Homer
Julius Caesar by Shakespeare
Hamlet by Shakespaere
Oedipus Rex by Sophocles
Huckleberry Finn by Mark Twain
The Great Gatsby by F. Scott Fitzgerald
The Grapes of Wrath by John Steinbeck
The Death of a Salesman by Arthur Miller
The Catcher in the Rye by J.D. Salinger
One Flew Over the Cuckoo's Nest by Ken Kesey
Oliver Twist by Charles Dickins
Crime and Punishment by Fedor Dostoevsky
Les Miserables by Victor Hugo
Madame Bovary by Gustave Flaubert
If you want books that will "enhance" your thinking, read some of these (and consider it an accomplishment if you can read and fully understand any one):
Utilitarianism by John Stuart Mill
On Liberty by John Stuart Mill
A Critique of Pure Reason by Immanuel Kant
Meditations Rene Descartes
A Theory of Justice by John Rawls
The Republic by Plato
Walden by Henry David Thoreau
The Origin of Species by Charles Darwin
In all honesty, I haven't fully read any of those from the second category, though I have read many passages from all of them.