Absolutely her ideas about are still applicable today. We live in a society that seems to be focused on the idea of me first. In addition, life is not fair, and the sooner people come to accept that the better off our lives will be. With that in mind, I always tell my kids that they can't control what life throws at them, but they can control how the handle it. They are in control of their own responses.
Let's begin with a good defiition of her philosophy. She called it Objectivism:
Objectivism holds that reality exists independent of consciousness, that man has direct contact with reality through sense perception, that one can attain objective knowledge from perception through the process of concept formation and inductive and deductive logic, that the proper moral purpose of one's life is the pursuit of one's own happiness or rational self-interest, that the only social system consistent with this morality is full respect for individual rights, embodied in pure laissez faire capitalism, and that the role of art in human life is to transform man's widest metaphysical ideas, by selective reproduction of reality, into a physical form—a work of art—that he can comprehend and to which he can respond emotionally. (very nicely done by the Wikipedia)
Now to your question: is her philosophy relevant today? Look around you and look into yourself: does it make sense?
From my own perspective, yes it makes a lot of sense. I was quite moved by her works, and by The Fountainhead the most. The book validated things I had already concluded about reality: the world is real and sometime harsh and indifferent; it is not created by the individual. And it is up to each individual to get out of reality as much as he can for the sake of his own freedom and happiness.
It certainly sounds like a basically selfish philosophy, but that's just a reality of existence: all organisms are born into a world that already exists, and they all have to find a way to survive and thrive that is scessful for for them. Otherwise they will wilter and perish. In Rand's view, no one has to step on anyone else's toes in his pursuit of happiness as long as he is honest and true to his own particular path and creativity.
So look around you: isn't that very much like the modern world as it exists today?