Amoral characters I get. It's part of the game, part of it's history and kind of a natural development as soon as you start throwing dice. But I'm really annoyed by players who want to play Evil Characters (TM) because they think it's cool. Just like it's totally indifferent if you play the good guys or the bad guys in World of Warcraft. Where the hell did that come from? Goths? Movies? The satanic panic and the sudden need to be not explicit? Is evil now just a selection of sinister clothes and make-up?
Well, it's obviously connected with the general lack of understanding the term Monster nowadays (which is directly derived from how THE GAME is played). And that's actually sad.
So this is about the necessity of evil in a game
For most people the Monster tag is enough to kill and loot. They don't need to know what ill deeds the monster actually might have done, they just assume it's justified enough to actually slaughter someone. I know, I know, some bones might be in the flavour text or whatever. My favourite has to be the proverbial Aura of Evil. "Don't look any further, son! Your GOD tells you here dwells evil! So fight the good fight and KILL THEM ALL!!" That's why the oh-so-popular Evil as Alignment was a stupid idea to begin with and helped degenerating our perception of the idea behind the word "evil" to something you can side with, to something socially acceptable or even desired.
Amoral or Evil, what's the difference?
You might google EVIL and find that it is mostly argued in a context of morality and/or perspective, with the individual mostly disconnected from the deed. But that's not argued in a narrative context. There is some truth in the notion that playing in a fictive world gives you more freedom of action. And that's what this is about. Amoral behaviour is, in game terms, within that freedom - doing evil is not. The Game being fiction changes the scope of what is acceptable, but it doesn't negate it.
Let me illustrate with another example:
Knowing this is happening in a tv show makes it far more funny than it would be in reality. Although it is disscusible what is funny or how cruel jokes are allowed to be, the fact that nobody is harmed by telling a joke is what I was aimig for. Amorality is allowed to be funny that way, but seeing, say, a staged rape on TV could never be seen in a positive light with most people. To find and define that line is one of the things a mature DM might want to do (and if it's just to be aware of it).
Let monsters be MONSTERS
As a DM, one should never forget to integrate the consequences of evil deeds into a setting. That's no easy task, it needs tact and it involves themes and ideas most people don't like to think about. But, for me at least, it's one of the responsibilities of being a DM. And it's one of the greatest narrative tools a DM might muster. If you want your players to take position against something or feel horror and tension, lead them out of their comfort zone, show them the "dark side" (and if it's only a glimpse...). It gives a world depth and variety.
So I try not just to go with the label evil and describe the results of the deeds instead, make it part of the story. And if a player wants to go down that road, I'm prepared to narrate him the consequences of his deeds...