1. Criticisms leveled against Consequentialism.
Consequentialism is based on the consequences of actions. It is sometimes called a teleological theory, from the Greek word telos, meaning goal. According to consequentialism, actions are right or wrong depending on whether their consequences further the goal. The goal (or, "the good") can be something like the happiness of all people or the spreading of peace and safety. Anything which contributes to that goal is right and anything which does not is wrong. Actions are thought to have no moral value in themselves (no rightness or wrongness), but only get moral value from whether or not they lead to the goal. John Stuart Mill was a famous consequentialist. Consequentialists would say that killing people is not right or wrong in itself, it depends on the outcome. Killing an innocent child would be a bad thing because it would decrease the happiness of its family and have no good results. Killing a terrorist would be a good thing because, although it would upset his family, it would make people safer.
The main criticism of consequentialism is that it would allow any action in pursuit of a good cause, even actions that most people would say were clearly morally wrong, such as torture, killing children, genocide, etc.
2. Criticisms leveled against Deontology
The word deontology comes from the Greek word deon, meaning duty. According to this theory, it is your duty to do actions which are right and not do those which are wrong. Actions are thought to be right or wrong in themselves. For example, killing people and lying are wrong, sharing with others who are in need is right. Immanuel Kant was a famous deontologist.
E.g. While trekking in the Andes you come across a guerilla leader who has captured 20 local villagers. The guerilla says if you will shoot one hostage he will let the other 19 go free. If you refuse to shoot, he will kill all 20. In the thought experiment the guerilla leader is telling the truth and you have only two choices: to shoot, or to refuse. Choose to shoot, and you are a consequentialist, motivated by saving the 19 innocent people. Choose to refuse, and you are a deontologist, motivated by the fact that it is always wrong to kill an innocent person.
The main criticism of deontology is that it is selfish, a way of avoiding getting your hands dirty (in a moral sense) while still allowing terrible things to happen. For instance, in the thought experiment you would not have shot anybody but 20 innocent people would still die. You could have prevented this outcome if you weren't afraid to take any guilt on yourself.
3. Criticisms of Utilitarianism
By far and and away the most common criticism of utilitarianism can be reduced simply to: "I don't like it" or "It doesn't suit my way of thinking". For an example of this, here's something from someone who might prefer to remain nameless.
"Producing the greatest good for the greatest number is fine as long as you are not hurting someone you really love in the process. For instance, with the trolley situation, I would rather kill 5 people on the main track than my mother on the spur track. Utilitarianism runs into problems when sentiment is involved!!"
Utilitarianism is alleged to be faulty in the way it requires us to think about all kinds of actions - to apply the felicific calculus in disregard to any feared distaste of the result. For example, some issues or potential actions are (to a non-utilitarian) "morally unthinkable":
Utilitarianism does indeed have something to say on this issue - otherwise it would suggest that the life of this extra individual was of no importance. I suggest it as a virtue of utility, that it does not arbitrarily discount value depending on some detail of the situation: all interests count - simply and fairly. The fact that opponents of utilitarianism admit that they won't even...