I've read all of Atlas Shrugged, and about the first 1/3 of The Fountainhead. Sure, there are plenty of individual Ayn Rand quotes that I agree with, and many of her ideas ring true in an isolated context, but this has nothing to do with the validity, or efficacy, of the "philosophy" of objectivism, as a whole. I can find quotes and ideas that I agree with, from just about any book, philosophy, or ideology, regardless of how incorrect the work is as a whole.
I have no idea how many people here have actually read Ayn Rand, but it was very popular among people in college when I read it. In my experience, a pretty good portion of educated people have read it at one time or another.
When I read it, at 19, it appealed to me greatly, and I held objectivism as a valid and true concept for probably a couple of years. The concepts appealed to me as someone who had left home at 18, was financially independent, and had gotten into a good college a year out of high school, all based on my own work and merit, without anyone's help. Objectivism appealed to my sense of superiority because of my independence compared to the other students around me. This, of course, makes sense at a time of life when we are all emotionally immature, despite our experiences or accomplishments.
At the core, regardless of any particular tidbits that might have merit, objectivism fails because it discounts empathy as a valid concept. It tries to eliminate the one attribute that actually makes us human. People are emotionally creatures, not rational ones - although we may be able to think and act rationally, the experience of being human will always be emotional.