Villains who read "Atlas Shrugged" might identify with the protagonist characters: powerful, smart, sexy, and separated from the masses. The dedicated reader might move on to learn more about Objectivism, the philosophy developed by the author.
Objectivism's core tenet is that knowledge and values are objective (hence the name). What most people think of, though, is Objectivism's views on altruism (uniformly negative) and the free market (uniformly positive). Ayn Rand was born and educated in Russia, but moved to the United States in her youth. Apparently she fell in love with capitalism on the way, and her experiences growing up soured her on any sort of collectivism or communism.
"My philosophy is the concept of man as a heroic being, with his own happiness as the moral purpose of his life, with productive achievement as his noblest activity, and reason as his own absolute," she writes. Most supervillains could get on board with the first half, and are still with you depending on how you define "productive". Many budding Objectivists would not be fine to hear that Rand sharply criticized "hedonists" and "whim-worshipers", which describes a lot of villains I could name. Plus, Objectivism regards the initiation of force as immoral, which, y'know, is what we do all day.
I don't think it's correct to classify Rand's philosophy as prizing "selfishness" the way most people think of it today. Rand promoted people doing useful things - but they were simply expected to also get paid for it. Her heroes are titans of industry, builders, manufacturers, and so on. They contributed to the greater good of society, but Rand was very insistent that all such contributions be justly rewarded by the free market. Because of this, Objectivism is actually much more of a superhero thing.
Rand's feelings on the free market are a little more accessible for villains, since a black market, backed up enough powerful crime kingpins to keep everything fair (except for them) is as close to a "free" market as you can probably hope to get. Government regulation, international trade, and so on put a very big thumb on the scale when it comes to legal markets.
All told, the more cynical of us regard Objectivism, and Rand's works promoting its ideals, as a sort of capitalism fan fiction. The philosophy encodes many of Rand's particular quirks (Murray Rothbard relates a story in "The Sociology of the Ayn Rand Cult" that one of her followers considered smoking to be a moral obligation of the system) and she was very clearly the person at the center of the system, rather than one promoter of many. It's ironic that her worst experiences in Russia would later be mirrored in the Objectivist community, such as periodic "purges" (though presumably non-fatal ones).
Rand's efforts to promote Objectivism were ultimately successful enough to get the attention of people like the chairman of the Federal reserve, and prominent senators and VP candidates. If appealing to the interests of such people is part of your program as a villain, you should give some thought to learning more about Objectivism. But since the Fed chief testified that he'd badly misjudged what business greed would do to the American economy, I'd advice giving Rand's advice on capitalism a pass.
Objectivism continues today under new management, and has changed direction a few times since Rand's death. Like a buffet, the aspiring supervillain may not like everything that's on the menu, but may find enough to fill a plate.