In addition to yesterday' interesting comment thread on the subject, Jake Young and Noumenal Self have defenses of their respect for Rand. I particularly found this bit, from Young, interesting:
She validates the individual and the power of the individual human mind. In Atlas Shrugged, she describes a world where the intelligent and the capable have made clear that they are not willing to be exploited by the violent, the ignorant, and the incompetent. They argue that this is a world that can be grasped and improved by an individual intelligence and all that is required is the application of effort and logic. As a scientist, a physician, an intellectual, and a human being, I find that appealing. I am neither the strongest, nor the most attractive, nor the richest, nor the most socially gifted kid in the room, but I am sure as hell capable of using my mind. Rand argues that this is all that is required for happiness.
I tend to not think much about philosophy as a form of self-validation, but it doesn't strike me as an obviously silly application, particularly for those who've long since rejected the comforts of religion.
Young also offers some hypotheses as to why people hate Ayn Rand so much. My short answer is that I don't merely find her worldview and premises unconvincing, I find them ugly -- which isn't to say those who respect her work interpret it as I do.