Neutral evil characters are the sort who will do whatever serves their own best interests. As far as they are concerned, that is all that matters. It doesn’t matter what they need to do in order to do it, that’s what will be done.
Interestingly enough, it’s this alignment that gets dubbed as “true evil”. Whereas you would think that “chaotic evil” would take that spot. I suppose it’s similar to how “neutral good” could arguably be seen as “true good” as opposed to “lawful good”.
The flavors of neutral evil characters vary. Some are just egomaniacs who see themselves as above any sense of morals or laws (though they will often use said laws when it suits them to do so). Others are just amoral. They aren’t malicious, they just don’t care one way or the other. You can also come across more actively evil characters who still work to serve their own interests, but know full well that what they are doing is wrong and choose to do it anyway.
Both Marvel and DC Comics have major villains that fall under this category in Wilson Fisk (aka The Kingpin) and Lex Luthor. Both are corrupt businessmen who do what they need to in order to get more power. They will break the law without remorse, but they will also manipulate that same law in order to get out of trouble.
Spider-Man’s nemesis, the Green Goblin, also fits this bill as the Goblin persona often makes a point to do things that will improve Norman’s status. Of course, Norman isn’t the most moral of people on a good day, but that element of his fractured psyche takes it to a whole new level.
Another excellent example of a neutral evil is Alex Krycek from The X-Files. He worked with and betrayed just about everyone in the show over the course of the series depending on what his goals were at that time.
South Park’s Eric Cartman is also a pretty solid example of a neutral evil character. He uses chaotic elements as well as more lawful elements on a whim in order to manipulate people into helping him accomplish his goals.
In a more general sense, a lot of hit-men and con men fall under this category as they generally do what they do for profit and make a point to say that it’s only business.
Neutral evil is a tough alignment to maintain in a tabletop group as other members are often heroic people doing heroic things. As such, it becomes tough to figure out a way to maintain the alliance with the group without becoming too heroic.
They can make for compelling characters, though. Even if it is tough to pull off in role playing, they are fun to watch or read about.