Ethical egoism is the view that one ought to do what is in one's own self-interest, if necessary to the exclusion of what is (or seems to be) in other people's interests. This can be contrasted with both altruism and psychological egoism. A philosophy holding that one should be honest, just, benevolent etc., because those virtues serve one's self-interest is egoistic; one holding that one should practice those virtues for reasons other than self-interest is not egoistic.
Ethical egoism tends to be a rare stance among philosophers. Many contend that the view is implausible on its face, and that those who advocate it seriously usually do so at the expense of redefining "self-interest" to include the interests of others. An ethical egoist might counter with the assertion that furthering the ends of others is sometimes the best means of furthering one's own ends.
Among philosophers of note who might be called ethical egoists are Friedrich Nietzsche, Ayn Rand, and Max Stirner. Some, such as Thomas Hobbes and David Gauthier, have argued that the conflicts which arise when people each pursue their own ends can be resolved the best for each individual only if they all voluntarily forgo some of their aims — that is, egoism within a society is often best pursued by being (partly) altruistic.
As Nietzsche (in Beyond Good and Evil) and Alasdair MacIntyre (in After Virtue) are famous for pointing out, the ancient Greeks did not associate morality with altruism in the way that post-Christian Western civilization has done. Consequently, it is sometimes said that Greeks like Aristotle (for whom pride was a virtue) were ethical egoists. It would be more accurate, perhaps, to say that the issue of altruism vs. egoism simply did not arise for them in the way that it does for us, or for some of us. Aristotle's view, for example, is that we have duties to ourselves as well as to other people (e.g. friends) and to the polis as a whole.