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.
There have been only a few ethical egoists among professional philosophers, but in the wake of Ayn Rand's nonfiction (she wrote a collection of essays called The Virtue of Selfishness), there have been a number of attempts to make ethical egoism widely respectable. The consensus among professional philosophers seems to be that the view is implausible to begin with and that those who advocate it seriously (as "enlightened egoists") do so only at the expense of redefining what self-interest amounts to (including, as it is made to do, the interests of some other people or all other people at some times).
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 ourselves as well as to other people (e.g., friends) and the polis as a whole.