"Evil" is kind of a subjective term.. I mean in the eyes of some champions, they are evil, like in the others they aren't.
Champions that are genuinely evil probably (in my opinion) would be:
: He's insane, he went insane from being alone and now he literally wants everyone to bow before him and his power. Remember, he's one of the most powerful Black Mages in Valoran.
: Is a demon, and by nature, demons are evil. He feeds off the misery of others, so Tahm Kench is pretty self-explanatory.
: Murders people just for fun.
: Tricks people into worshipping a spider god, which she feeds them to Vilemaw in turn for immortality.
: Thresh, even in life, was not a good person. He literally tortures people to death, and when they die, takes their soul and tortures it. Completely sadistic and does it for the sheer pleasure of breaking them.
: Tyrant 'ruler' of Bilgewater before being dethroned by Miss Fortune. Kills people just for disagreeing with him/being in the wrong place at the wrong time.
: Literally tricked Azir into doing an ascension ritual so he could gain the power over others, was the cause (or one of) of the fall of Shurima.
Now for Factions/Champions that can be seen as evil by others, but might not necessarily be evil.
I'm not really going to put Noxus on this list because Noxus is all about power. If you are weak, you don't deserve to live. Saying that the champions are 'evil' from here is purely the opinion of the beholder. To a lot of Noxians, Demacia is the enemy, thus 'evil' to them.
Now, I'm not going to list a lot of Shadow Isles champions because in reality they all kind of follow the will of the Shadow Isles, which is to seek out and kill others to bring into their undead rankings.
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: They both are fighting for their beliefs in how their society should be built upon. In Morgana's eyes, Kayle is an evil dictator that wants to rule her people with an iron fist. In Kayle's eyes, Morgana is someone who wants to disrupt order for freedom and thus sees her as evil. Morgana does use dark magic, but uses it to 'set her people free.'
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: Singed and Warwick are mercenaries that get hired to make chemicals for war and kill everyone. If they get paid, who cares if there is death?
Void Champions: The Void can be seen as evil by almost every other faction, but creatures from The Void survive by killing, consuming, and adapting. In the case of Cho'Gath/Kog'Maw, eating is all they do. Kha'Zix does it to become the perfect hunter, and Vel'Koz does it to seek unlimited knowledge. Their ways of going around it are not the best, but that doesn't necessarily make them evil. Now the overall goal of The Void, which is to invade Runeterra and devour it completely might be pretty evil...
: He's a spirit of nature, his nature is to destroy things and purge it with fire. Does that make him evil? Not really, it just makes him a drive of nature.
: Her masters are the Watchers, powerful beings that gifted many of the ancient residents with Iceborn power at the cost of their freedom. Really, she works to return her masters to power, but doesn't make her completely evil.
: He loves war. He loves joining in on wars and bringing one side power, just for the joy of watching the war go on and death reign. I wouldn't consider him evil though.
But yeah, please remember that everyone has their own opinion on things and not everyone percieves evil the exact same way as someone else. In my opinion I think that Demacia's government is pretty evil, suppressing its people and all for the sake of image.