I've read Atlas Shrugged more than once. I've also read The Fountainhead and The Virtue of Selfishness. For a few years in high school I was an unabashed Randite (read: obnoxious, loud-mouthed asshole).
The simple fact is that Objectivism, for all of its many flaws, is deeply appealing because it presents a simple, black and white view of the world. Whereas Granny Weatherwax says "Ain't no shades of gray. Just white that's got grubby.", Rand said that white a little tarnished is no different from black. Go 100% or go home.
She peppers her fiction with dramatic archetypes. Just from Atlas Shrugged you have the ideal man (Galt) four flavors of the nearly ideal man (Rearden, Frisco, the pirate, and the philosophy teacher), the ideal woman (Dagny, whose ideal nature is demonstrated by the fact that, intelligent and hard working, she also wants to be dominated by her men) several men who deliberately invert the ideal (Dagny's brother and a few politicians), and several people who believe in the ideal but fail to live up to it (the scientist who taught Galt, the woman who married Dagny's brother).
And the thing is that Objectivism really does believe that people should not merely strive for that ideal, but actively embody it, and that anyone who fails to do so is morally wrong. At the end of the day, Objectivism was a cult (http://www.lewrockwell.com/rothbard/rothbard23.html)and Atlas was its bible. Rand was its Jesus and Nathaniel Branden its Saint Peter. When Branden was excommunicated, the cult fell apart because, as thorough and author as she was, Rand was neither a reader, nor a leader, nor a thinker. Occasionally, someone will still get sucked into it, but it hasn't been what it was in the 60s.
As for the stated beliefs of Objectivism:
Metaphysics - I agree that existence exists (that is to say, there exists an external and separate reality from each of us) and that each of us is a conscious, moral agent. I disagree that everything has a specific nature or identity. Yes, as Sartre said, "Nothing can exist only partly" (which is what I believe this part of the Objectivist metaphysics is trying to say), but beyond the existence of an object or thing, it is outside actors who imbue objects with use or identity beyond the mere fact of their existence. In other words, A is A, but it's not just A.
Epistemology - Rand was an empiricist (she called it reason but that's a woefully inadequate description, as actual philosophers disagree on the utility of reason and on how it works), arguing that all knowledge is fact-based, built on a study of reality with which we connect through our senses. She argued that we have no in-built knowledge or ideas. I don't fully agree, because we have a number of built-in shortcuts for dealing with the world; we innately seek and assign agency where none need exist. How often have you gotten angry with an inanimate object for not working right? Even as infants, we assign such; show an infant a moving image of two objects, one following the other, and it will register surprise if the one stops following. Children tell that inanimate objects have purpose, assigning agency to the world around us; rocks are for animals to scratch themselves, clouds are for raining. These are just a few demonstrations that the human brain doesn't sift through our perceptions in a logical, step by step basis. We take short cuts and make quick assumptions. For the most part this helps us out (you don't really need to analyze a tiger, buddy, just leave it alone), but for complex issues it can get us in trouble.
Ethics - I agree with Rand that there is no objective or external source of goodness (the platonic ideal) nor is goodness some sort of natural function (the Aristotelian philosophy that influenced Catholic doctrine via Thomas Aquinas), but rather a function of human behavior. Rand argued that moral good is that which sustains life, moral evil is that which hinders it, and above all both are informed by rational choices about objective reality. I disagree, in that moral behavior arises from biology. We have in our brains two separate decision-making processes for moral behavior, an empathic core (don't kick the baby!) and a utilitarian core (kill the one to save the ten, it's just sense) and our moral decisions come after a tug of war between the two. We are certainly not a rational animal, as Rand would have it, but a rationalizing animal, using our logical faculties not to make decisions but to justify them after the fact.
Our moral and ethical nature is not built around the survival of the individual, but around the survival of the individual within the context of the survival of the group, and not just the group as a collection of individuals, but the group as an entity in itself which will continue to exist after all of the current members have died off. This "collectivism", as Rand would have called it, is anathema to Objectivist philosophy, but is paramount to the human condition. Unfortunately for Rand, the Kantian ethic "do only that which you can will as a universal rule" doesn't actually work. Very nearly everything you subject to that slippery slope argument falls into a black pit of reductio ad absurdum and cannot possibly be construed as a moral good. Boundless self-sacrifice by everyone would lead to everything falling apart in a way that boundless selfishness would not, but you wouldn't want to live in a world of sociopaths any more than you would a world of nothing but sacrifice. Moderation in all things (even moderation, bitches!).
Politics - I really disagree with Rand. The individual is not the be all and end all of human existence (which makes the Republican love affair with Rand hilarious) and individual efforts not the only method of achievement. She honestly felt we could get by with private police and fire protection, which is farcical on its face. There was a private fire company in Rome. They showed up, got the owner to sell cheap, then put out the fire. The fact is that cooperation for mutual benefit is, on its face, a perfectly valid method for achieving success. She accepts this in the private sector for corporations, but weirdly denies it in politics. Why is it that a cartel by the name of OPEC is in some way a good and moral agent, but a cartel by the name of government some sort of villain?