I agree with @nikipedia. What’s wrong with being selfish?
After further thought, I think that the answer to this question is, yes, there is such a thing as a non-selfish act. But this realization has brought another question to my mind. Is such an act desirable?
In order for an act to be non-selfish, the doer of said act would have to glean no benefit (or at least perceive no benefit from his act). In other words, his best self-interest would be harmed by the act. Consider the act of sacrificing one’s life for an unworthy person; someone whose benefit to society would be less that that offered by the doer of the act. For instance, a would-be successful cancer researcher jumping in front of a train to save a child-molester. He loses his life, and society suffers the loss more than what is saved. This is always the case when doing something outside of one’s own rational self-interest. If the scientist had rationally considered his actions, he might have realized many of the shortcomings of such a choice. Not only has he lost his life (certainly counter to his self-interest), but by doing so, he has saved the life of someone who may then turn around and harm the scientist’s own offspring (made that much easier by the fact that he is not around to protect his children). And of course, there is the obvious—it’s hard to cure cancer when you’re dead.
That’s not to say that sacrificing one’s own life for another is always unselfish. If the situation were reversed, and the child-molester’s offspring were dying from cancer, his self-interest might lie in saving the cancer researcher, even at the expense of his own life.