Answer: Ayn Rand was a radical thinker, i.e., one who went to the root of long-standing philosophical problems. She was self-consciously opposed to many of the ideas of most of the well-developed Western philosophical traditions ( such as Platonism, Kantianism, German Idealism, Pragmatism, Humean Empiricism, and Existentialism). As an advocate of objectivity and rational selfishness she was opposed to the key teachings of virtually all religions.
Read our Q&A archive online to see some of the contrasts (I could not even scratch the surface here). To go more in depth read "This is John Galt Speaking" or "For the New Intellectual" in the book of that name by Ayn Rand for Objectivist attacks on prominent views. Nathaniel Branden's "The Moral Revolution in Atlas Shrugged " is another good source, as is my own "Radical for Capitalism." I also have an introductory course, "The Essence of Objectivism," on CD, that contrasts Objectivism with many prominent ideas. (All the above are available from The Objectivism Store. )
There is something of a dearth of good, published criticism of Objectivism . You can find some in The Journal of Ayn Rand Studies or in TOC's own Objectivist Studies monographs . There is a valuable website that provides links to online criticisms of Objectivism , and some of these in my view are good criticisms, in the sense of being based on a fair reading of Rand's meaning and raising worthy questions.
A number of books sharply critical of Objectivism have been published over the years (all these can be researched through the Objectivism Reference Center , which has the critics links). Several are by Christians of a certain stripe, including books by John Robbins and Michael Yang. "The Philosophic Thought of Ayn Rand" by Douglas Rasmussen and Douglas Den Uyl contains philosophical critiques of Objectivism of varying quality. "The Ayn Rand Cult" by Jeff Walker collects every attack or scurrilous rumor and slings every bit of mud against Objectivism as can be found. It's a self-contradictory and sloppily researched hash, but it serves up of plenty of vitriol, if that's what you are looking for. None of the book-length criticisms of Objectivism I am aware of is good: none combines basic standards of scholarship and a sound understanding of Objectivism with a basically rational approach to criticism.