A moral dilemma is a situation in which it is difficult or impossible for a person to choose a morally good course of action. Dilemmas of this sort are the stuff of tragedy: a character (person) finds himself in a situation from which there is effectively no escape. If every possible action is evil, then there is nothing left to do but despair. Now, while there are certainly tragic situations in life, it seems to me that one consequence of the existence of a loving, almighty God is the exclusion of genuine moral dilemmas: i.e., situations in which a person cannot possibly choose to act or not to act without sinning. Which is to say that, given good character and a good understanding of what is going on, there will always be at least one "right" response.
Of course, our capacity to judge what is good is inhibited by disordered appetites, concupisence, and the ignorance which comes from sin. Thus many situations which do not actually present a grave moral difficulty may seem to do so if right action demands a higher degree of moral perfection than we presently embody. Generally situations presented as moral dilemmas depend for their problematic nature on a common misevaluation of various goods. Consider the following set of examples:
1. You really ought to have the hit new album by The Wilting Spoon, but you are presently broke. You could steal it, but stealing is wrong. Moral dilemma: Do you neglect your own human dignity by going without the new album, or do you steal it?
2. You have just been kidnapped by pirates and gradually starved for over a week, only to be deposited without food, money, or map in a vineyard somewhere in the world. You feel that you are about to surrender to death, surrounded by someone else's food. Do you steal it or let yourself die?
3. Aliens from Zobomb have decided to experiment on humanity and you are their latest subject. They present you with a five year old child and a hatchet and tell you that if you don't deliver his brain to them in three minutes the planet Earth will be annihilated with all its inhabitants. Do you sacrifice young Tommy to save humanity?
Each of these cases plays off of apparently competing norms. In the first, there's the naive egoist's impulse to self-gratification pitted against the self-evident fact that one ought not steal. This is easily resolved when we realize the actual value of having the album and its role in character growth, etc. etc.
In the second case, the norm against stealing is pitted against the will to self-preservation. It is tempting to say that theft is admissible here because of a "proportionate reason", but really Aquinas's solution (the devolution of property upon all of humanity in states of dire necessity) has the advantage of being reasonable and not opening up a can of (utilitarian) worms.
The third case is particularly difficult for the average person. It's tempting to look at all the lives potentially saved and "weigh" them against the life of young Tommy. A weird moralizing voice might even occur to you: "Do you really value your own conscience over the lives of billions?" And in many the response might be a kind of heroism: "I will murder the child and do this hard deed but all of humanity will be indebted to me for my sacrifice!" And yet to the trained conscience these responses are all clearly abominable. To murder the child would be to cooperate with evil, and what does it profit a man if he gains the whole world but loses his soul?
More signifcant, perhaps more interesting, than the resolution of these particular cases of conscience is the general fact that some situations are ugly and unpleasant to live though, though no guilt may directly accrue to the person who does so. The person who actually chose to spare Tommy's life and watch the world be blown away would certainly feel an untold amount of horror and pehaps guilt in the process. But this is due to the evil of the Zobombian aliens and not his own fault. Right action can even bring about a kind of despair, as when the pregnant college student realizes that she must leave school in order to care for the child she might otherwise have aborted. Such a choice involves the destruction of an entire future life and the sudden onset of a vast number of commitments and responsibilities, and the thought that one is doing the right thing would probably be little consolation. (Though the gift of a child ought to be a great one.) It is always tempting to believe that no right action could demand such a great amount of inconvenience. (Robert Bolt's play A Man For All Seasons is a great meditation on this problem.)