Any theory that gives pleasure a central role. The simplest form of hedonism in ethics is "whatever causes pleasure is right". Even that simple version immediately runs into trouble. Pleasure for whom? Average pleasure? Is that the median or the mean? How can you make interpersonal comparisons of pleasure, anyway? Or even cross-time comparisons for the same person? Is that pleasure in the short term, or the long term? Another summary of hedonism, "Pleasure is the highest good" avoids some of these complexities, at the cost of not saying anything of practical consequence.
Epicureanism is the best-known form of ancient hedonism. Epicurus identified pleasure with tranquility, and emphasized the "reduce desire" aspects over the "find lots of hot babes" aspects.
The utilitarianism of John Stuart Mill (of his own free will) is sometimes classified as a type of hedonism, since it judges the rightness of actions from the happiness that they lead to, and happiness is identified with pleasure. This is, note, a selfless hedonism; whereas Epicurus recommends doing whatever makes you happiest, Mill would have you do whatever makes everyone happiest.
Some of Sigmund Freud's theories of human motivation have been called psychological hedonism; his "life instinct" turns out to be the (startling!) observation that people pursue pleasure. But he muddies up the waters with various less plausible mechanisms, such as the "death instinct".
External links: The Internet Encyclopedia of Philosophy on:
Hedonism: http://www.utm.edu/research/iep/h/hedonism.htm Epicurus: http://www.utm.edu/research/iep/e/epicur.htm Mill: http://www.utm.edu/research/iep/m/milljs.htm Frreud: http://www.utm.edu/research/iep/f/freud.htm