I teach ethics, mainly business ethics, and here is a brief outline of some of the more prominent schools I discuss in class:
A. Ethical hedonism is the view that everyone ought to seek to obtain as much physical pleasure in life as possible. This has appeal because physical pleasure is an easily recognized value, something that we can all accept as good, so it is easily verified and that, in turn, makes it appeal to the scientific mentality that is so widespread in our age. (Jeremy Bentham is a most prominent ethical hedonist.)
B. Utilitarianism is the view that everyone ought to seek to promote the greatest happiness of the greatest number of (that is, most) mainly people but perhaps animals, too. Two types of utilitarianism have been advocated – act and rule – but only rule utilitarianism is popular. It requires that one identify a set of rules or principles to guide one's conduct, with the goal of promoting the greatest happiness of the greatest number (which is often referred to as the public or common or humanity's interest or welfare). (John Stuart Mill is the most prominent defender of utilitarianism.)
C. Altruists hold that we ought to advance the well being of others first and foremost – mainly other people but perhaps also animals. Two versions have been advocated – subjective and objective altruism. The first identifies what will benefit someone by reference to that person's desires or preferences, the second by reference to various facts about the person. (Auguste Comte is a famous advocate of altruism.)
D. Ethical egoism is the view that we ought all to promote our own well being, first and foremost. Some egoists are subjectivists, others objectivists – the first, as with altruism, identify what is good for oneself by reference to one's desires or preferences, the second by reference to one's thoroughly knowledge of oneself, one's needs, talents, and anything else important. (Max Stirner is a famous subjective ethical egoist and Ayn Rand is well known as an objective ethical egoist.)
Some less prominent schools of ethics include Stoicism (do not yield of emotions), Epicureanism (promote refined pleasures), asceticism (cultivate self-denial), the various religious schools of ethics and so on.