Virtue Ethics
Virtue ethics is really a family of views, not just one.
Virtue Theory: This kind of ethical theory goes back to the ancient Greeks who were ethical egoists. Plato argued that one should try to do the right thing, or be good, because it is in one's own self-interest. This is for several reasons. One is that he thought that good people had a much more pleasant time in the after-life than bad people. Another reason is that being good is good, i.e. intrinsically valuable (he uses a kind of poetry -- e.g. the image of the cave and Goodness as the sun -- to try to get us to see or feel this). Finally, he argues that being good is a matter not of doing this or that but of having a well-ordered soul. The well-ordered soul is ruled by reason (which knows that it is good to be good) in conjunction with spirit, which together dominate the bodily appetites. Plato seems to think that such a soul is good for two reasons: one is that it will get you whatever you want more effectively than a soul that is, say, dominated by animal desires (so it is prudent to have a well-ordered soul), and the other is that a well-ordered soul is harmonious or beautiful, "right" in some sense. So goodness has both prudential and intrinsic value. It is useful and beautiful.
Aristotle's idea of ethics is similar but expressed in different terms. He rejects the idea of Goodness as such, but he still believes that some things just are right for members of a certain species. Human beings should be human. And what makes us human, i.e. different from other animals? Reason. So, once again, we should be ruled by the rational (or thinking, or aware, or conscious) part of ourselves. We are also naturally social beings, he thinks. So we should avoid anti-social behavior. Irrational and anti-social behavior is imprudent (it will lead to dissatisfaction) but it is also unnatural and therefore "wrong".
What Plato and Aristotle have in common is a concern more for the state of one's soul (or mind or character) than for specific rules of conduct. According to Aristotle, ethics is not an exact science so we cannot calculate precisely what each person should do in each possible situation. There are too many variables to take into account (and even if we knew them all, only a truly good person would know what the right thing to do was -- cf. the question, What would Jesus do?). The most important thing is to have good character, i.e. to be virtuous. Then you will somehow know what the situation calls for.
What does it take to be virtuous? Which traits make up a good character? Those that are useful for getting what you want (e.g. courage, prudence, self-control) and those that are just plain beautiful, natural, or right. (In the 18th century David Hume defined virtues as characteristics that are useful or agreeable to oneself or to others, which is much the same idea.)
Another notable feature of virtue theory is that, since it focuses on character rather than action, it can include concern with feelings. For Kant, for instance, feelings are either irrelevant to ethics or else are there to be overcome. You cannot help how you feel, he seems to think, but you can help what you do, and that's what being ethical is all about: putting duty above personal feelings. Virtue theorists, on the other hand, tend to think that the feelings you have reflect on your character. If you get pleasure out of other people's misfortune, for instance, that usually means you have a flawed character, that you lack some virtue. On the other hand, if you have a good character you will naturally tend to do good deeds, and enjoy doing them. Kant would say a good deed done for pleasure has no moral worth. Many people prefer the virtue theory view of this issue.
Finally, note well: Virtue theorists do believe that certain acts are right and others are wrong. They are not relativists. But they are particularists, i.e. they believe that whether a given act is right or wrong sometimes depends on the particular situation you are in (a bit like act utilitarianism). In this sense ethics is situational, but there are still some absolutes.
Problems: Virtue theorists face various problems.
1) Exactly which traits are virtues? Aristotle thought pride was a virtue, but Christian virtue theorists think it is a vice. Christians think chastity is a virtue, but Hume derided it as "monkish."
2) What is the precise nature of each virtue? Is courage in a bad cause really courage? Does honesty mean never lying? Etc.
3) Why are the virtues good? This relates to problem number 1. Can ethics be reduced to the study of how to get what you want, no matter what it is? Surely not. But then we're left with the hopelessly vague idea of what is beautiful, or natural, or right. If we don't know what makes virtues good we can't hope to know what traits are virtues (i.e. good traits).
4) Are there any such things as character traits at all? Or is everything we do the result of situational pressures? This has been suggested by some psychologists, but it seems a mistake to think that any empirical study could show that there is no such thing as, say, courage, even if it can show that not many people have that virtue. There certainly is evidence that virtue is rare, as we see when social pressures to be good collapse (as in the former Yugoslavia and Rwanda).
Good features of virtue theory: If love and loyalty are virtues, then virtue theory seems to be closer to common sense than other theories, especially utilitarianism, on the question of impartiality. Utilitarians say we should be impartial. Virtue theorists tend to think it is good to be biased in favor of your friends and family. Secondly, virtue theory says it is good to do what you want, as long as what you want to do is good. This might sound obvious, but Kant would disagree (at least partly). So again, virtue theory sounds better than its rivals. James Rachels criticizes virtue theory for not telling us what to do, but Aristotle sees this as a strength of the theory. It does not pretend to be able to tell us what a wise and good person (such as Jesus or Socrates) would do in every possible situation. After all, we are not Jesus or Socrates, and perhaps their wisdom cannot be reduced to any kind of theory. Instead virtue theory encourages us to become more like Jesus and Socrates. Then we won't need to turn to a philosophical theory to make our decisions for us.
Final verdict on virtue theory: Rachels also complains that the idea of virtue is too broad. Virtue theory almost seems to say, "Be good and do the right thing." But how helpful is that? This objection is at least close to problem 3 above. It is indeed a serious flaw in virtue theory. This does not prove that questions of character are irrelevant to ethics, but it is a problem that any virtue theorist ought to address.
Virtue Without Theory: Virtue theory became fashionable (slowly) after the publication in 1958 of a paper called "Modern Moral Philosophy" by Elizabeth Anscombe. Anscombe condemned all modern ethical theory as either corrupt or senseless. It makes sense, Anscombe argued, to think in terms of right and wrong, of what one may or may not do, etc. if one believes in God. "Wrong", for instance, might then mean "forbidden by God." And it's bad to do what God has forbidden either just because He is God (divine command theory) or else because He created us, offers us salvation, etc.. If you do not accept God's existence, though, or some God-substitute such as Plato's form of the good or Aristotle's vision of nature with in-built goals and purposes, then what can it possibly mean to say that something is 'right' or 'wrong' etc.? You might mean that it is convenient, or generally approved of by society, or something like that, she says. But that is not a good way to decide what is right and what is wrong. So utilitarianism is basically corrupt and the Kantian idea that there are some things we just categorically must (or must not) do is basically senseless. Instead of such modern theories Anscombe recommended something more like Aristotle's virtue theory, but she pointed out the big problem that this theory faces (see above).
What does she recommend then? Since Anscombe was a Catholic it is pretty safe to assume that she would suggest we base our ethics on old-fashioned religion. The best (other) alternative is to try to solve the problem that Aristotle's theory faces. But nobody has done that yet, and perhaps they never will. Our best bet seems to be to avoid, as much as possible, concepts like 'right' and 'wrong' (which Bernard Williams calls "thin") and instead use "thicker" concepts like 'brave', 'unjust', etc. as much as we can. This kind of virtue ethics need not focus especially or exclusively on the character of the person doing each act. But it will focus on the character of the act itself. And it is likely to include Kantian and utilitarian concerns as well. Is such an act rational (Kantian)? Does it promote happiness (utilitarian)? And so on. Which concerns of this type are relevant to ethics? Probably all of them. That's why there are so many Kantians and utilitarians around. Which is most important in each situation? Perhaps God alone knows. Common sense suggests that consistent Kantianism leads to problems and that consistent utilitarianism does too. It might be that ultimately each individual must decide each issue for him or herself. How different is this from just letting your conscience be your guide? Perhaps not very, so long as the conscience belongs to a person that has been raised well, is well informed about the issue, and is reasonably impartial. These qualifications are important. Simply following your conscience is otherwise not likely to guarantee good behavior. Think of Huckleberry Finn, whose conscience told him it was wrong to help a runaway slave. Ethics might not be reducible to reason alone, but sometimes it's good to think about what you do.