To sum up: Egoism, if we merely understand by it a method that aims at Self-realisation, seems to be a form into which almost any ethical system may be thrown, without modifying its essential characteristics. And even when further defined as Egoistic Hedonism, it is still imperfectly distinguishable from Intuitionism if quality of pleasures is admitted as a consideration distinct from and overruling quantity. There remains then Pure or Quantitative Egoistic Hedonism, which, as a method essentially distinct from all others and widely maintained to be rational, seems to deserve a detailed examination. According to this the rational agent regards quantity of consequent pleasure and pain to himself as alone important in choosing between alternatives of action; and seeks always the greatest attainable surplus of pleasure over pain—which, without violation of usage, we may designate as his 'greatest happiness.' It seems to be this view and attitude of mind which is most commonly intended by the vaguer terms 'egoism,' 'egoistic': and therefore I shall allow myself to use these terms in this more precise signification.
(Henry Sidgwick, The Methods of Ethics, 7th ed. [Indianapolis: Hackett Publishing Company, 1981], bk. I, chap. VII, sec. 2, p. 95 [first published in 1907; 1st ed. published in 1874])
Note from KBJ: Sidgwick, a utilitarian, is one of the few philosophers to have taken ethical egoism seriously. It is part of what makes him a great philosopher. Many philosophers today are prejudiced against ethical egoism. James Rachels, for example, calls it "wicked."
Note 2 from KBJ: Egoism, as understood by Sidgwick, is similar to utilitarianism in all respects but one. Both are consequentialist (in determining rightness, only consequences matter); both are monistic (there is only one intrinsic good); both are hedonistic (pleasure is that good); and both are maximizing (the right act is the act that maximizes the good). The only difference is whose pleasure counts. To a utilitarian, everyone's pleasure counts, and equally so; to an egoist, only the agent's pleasure counts. Utilitarianism is impartialistic; egoism is partialistic. Indeed, egoism is maximally partialistic.