A lot of libertarians were influenced by novelist Ayn Rand. It's important to keep in mind that she wrote her novels in a different time, when it was radical to suggest that profit and self-interest might not be bad. While I think it's possible to get some useful things out of her novels--a sense of outrage at the destructive capability of government intervention, for example--there's not a lot more to be learned from them. I read it in high school, and was briefly excited. It opened my mind to different ways of thinking about the world. I soured on the philosophy itself pretty quickly, however.
Charles Murray has a new review of two recent books about Rand, and it has some great criticism. When I look at the lives of the people who created and tried to live by the Objectivist philosophy, I don't really see anything that makes me want to jump on board. They seem miserable, hypocritical, self-deceptive, and prone to witch-hunts and purity tests that seem more like religion than rational philosophy.
There are plenty of knocks against the philosophy itself. David Friedman points out that her derivation of "ought" from "is" doesn't follow. Bryan Caplan suggests that her philosophy is at adds with evolutionary psychology (the same occurred to me after reading Nathaniel Brandon's biography a few years ago; they seemed to think human nature could be overcome by pure rational thought, or perhaps that human nature was pure rational thought--but evolution selects for reproductive success, not rationality. The results were affairs that ended badly.). Roy Childs pointed out years ago that the logical conclusion of her philosophy is Anarcho-Capitalism, not minarchy. A quick Google search will show you other critiques of Objectivism, although some of them are weak.
(SPOILERS for Atlas Shrugged below)
It has also always bothered me that Galt's Gulch is hidden by some kind of holographic screen, which is a pretty serious public good, yet we're also told that there's no taxation. So who pays for the screen? Surely it's not charity; that would be, in Rand's view, evil. The rest of the economics is pretty laughable, too--even with a motor that pulls static electricity from the air, they could not have a complex, wealthy modern society without heavy trade with the outside world, for natural resources at the very least. They'd be lucky to achieve subsistence. It reminds me of Art Carden's critique of the end of Wall-e: If they decide to try farming, 90% of the population will die within a year.