We discussed a number of issues about the proper formulation of this sort of utilitarian view. The general outline of a utilitarian view is that the right action is that action, from among those available to the agent, which will produce more intrinsic good than any alternative action.
This leaves open a number of questions, among them: (1) what is intrinsically good? Answers include hedonism (pleasure is the only intrinsic good) and preferentialism (what's intrinsically good is the satisfaction of our preferences -- roughly, getting what you want, where what you want may or may not be limited to pleasure). There are various ways of refining these views; for instance, we might say that what matters is not the actual preferences of an agent, but rather the preferences the agent would have if fully informed of the relevant facts. (2) whose good counts in the utilitarian calculation? All people, or only some of them? Only people, or other animals as well?
A. Distributive concerns. Utilitarianism is concerned with maximizing utility, but not with how that utility is distributed. One person's unhappiness can be outweighed by the happiness of others. As Rawls suggests, it seems to many that a just distribution should matter, not merely a high total utility.
B. Agent-relative permissions. Williams suggests that utilitarianism is incompatible with having personal projects or commitments. (The example of George illustrates this.) To the extent that one's projects and commitments are essential to one's self-conception, utilitarianism threatens to undermine one's integrity as a person. Williams's stress on the importance of such projects has affinities with Nagel's discussion of "reasons of autonomy" and also with Wolf's discussion of moral saints.
C. Agent-relative restrictions. In "War and Massacre," Nagel argues that there are absolutist or deontological restrictions on what it is permissible to do in the pursuit of overall utility. The one he stresses in that essay is a restriction on "fighting dirty." Other similar restrictions are discussed under the heading of "deontological constraints" in his essay "Autonomy and Deontology."
They suggest two main refinements. The first is to enrich our conception of the goods that consequentialists should maximize. Instead of simply maximizing pleasure or happiness or expected utility or something of the sort, consequentialists should try to maximize other goods as well, including autonomy and fairness.
The second refinement is a bit different in the two cases. Scanlon argues for a two-tiered consequentialism. Such a consequentialism will appeal to consequences in justifying certain general rules of behavior, for instance the claim that we ought to respect certain rights. But these rules of behavior rather than consequentialism itself will then guide individual decisions, and the rules may in fact place limits on what consequentialist reasoning can justify at the level of individual decisions. This is similar, as Scanlon notes, to rule-utilitarianism.
Railton offers a similar refinement. He argues that we should be objective rather than subjective consequentialists: we should recognize that constantly attempting to maximize utility is likely to lead to less overall utility than alternative strategies of decision-making, and therefore the thoughtful consequentialist will pursue nonconsequentialist decision-making strategies which are more likely to actually have the effect of maximizing utility.
Foot offers a more radical challenge to consequentialism, arguing that there is no such thing as the notion of the best available state of affairs. If there's no such thing as the best available state of affairs, there can't be a moral requirement to bring it about!
Such a broader conception of ethics would include attention to the virtues, states of character which enable humans to flourish. We've discussed in some detail one attempt to make this idea more precise, that of Alasdair MacIntyre.