I played a pair of evil characters in our recently concluded PF campaign.
(Due to group instability for a bit thanks to jobs/health/family/etc, the DM wanted everybody to have two characters. The idea was that if there were only a few of us on game night we'd still have a 4 person party. At 3 players only 1 person would be running 2 characters (we decided to rotate that duty). At 4+ players we'd choose one of our characters to be active that session.)
I did this for a few reasons:
1) I just simply had a really good idea for a pair of Lawful-Evil characters. (a chevalier & a divination wizard)
2) One of the players LOVES to play paladins. It's his favorite class. Unfortunately he's also really really bad at it RP wise. He almost always ends up falling (wich is not his intent). I decided to act as his foil. So I challenged him to be a better hero than me. I also challenged him to convince at least one of my characters to change their alignment - something he'd only be able to do through RP, over time.
And if something awful had to be done? Well, my characters aren't going to be harmed by getting their hands dirty.
3) SAVING THE WORLD. Extreme self-interest. Yeah, my characters are evil. And they each have plans. But those plans won't matter didly if the world is consumed by the Abyss!
Because that would be completely out of character for the evil PC in question?
Because there's something more pressing to do?
Because those goody-two-shoes
don't deserve it?
Because those goody-two-shoes are vital to the mission(s) at hand?
Because they are more useful to my own plans alive & equipped than dead?
Most of the evil acts my two characters committed were in their backstories. Just because they weren't currently doing anything (too much) worse than any other party member doesn't erase years of taint. Or automatically change attitudes & beliefs. Thus, still evil....
Besides, I WANTED the paladin player to stop me from doing evil things. So I'd set him up with oprotunities & provoke him.

To his credit he's why I wasn't doing things too much worse than the rest of the party.
As for killing me? Our characters (paladin vs chevalier) did trade blows a few times. Out-of-character he was reminded just how far ahead of him in system-mastery I am. In-character he learned that our characters fates were tied together (that was an awesome reveal). So we decided to shelve the all out PvP until
after we'd saved the world.

Still, until late in the campaign he viewed me as an enemy. From my PoV? He was a useful tool in my efforts to save the world.
It was noted after the campaign ended that neither of my characters had ever attacked a fellow party member 1st (as in initiating it, just winning the initiative roll is different), never stolen from the group, never cheated the group, nor betrayed them.