An article in the New York Times about Rand and Atlas Shrugged that is notable for the absence of the expected condescending sneering.
Rand didn't much influence my political philosophy, which was about the same before I read her stuff as it is now, but I do give her credit for two things. First, she indirectly persuaded me that caring about the success of strangers on sports teams that happen to carry the name of my city or school is a waste of time. This freed up thousands of hours for other endeavors more directly related to my own life. (I'm not an evangelist about this; if you enjoy rooting for sports teams, and think the opportunity costs are worth the enjoyment you get out of it, more power to you.)
Also, discussions of Rand typically focus on her political and moral philosophy, but, as the Times article suggests, she inspired a lot of people, of all political, religious, and social views, to raise their aspirations and expectations of themselves. In my own case, I had always done well in school, but never studied hard or paid much attention to my classes. It was after reading Rand, and being at least as inspired by her example as her characters (an adult immigrant who didn't know English becoming one of the most influential English-language novelists of all time, in part due to her sheer force of will) that I started to apply myself--I think I'm somewhat unusual in that I still work much harder as a tenured law professor than I did in school. (Whether Rand did me a favor, or whether I'd be better off in some sense as a slacker with lots of free time like I was in college, is admittedly an interesting question.)