There are SOOOOO many ways you can go about this, so I'll do my best to explain.
Basic:
Something basic, like being a mindless beast of destruction, can be your every day evil, these can range from wild animals driven crazy by the Big Bad to Demons and Undead summoned by the Big Bad.
Semi-Sentient:
These can be possessed people, or undead that are aware that they're harming people, but cannot stop themselves. These can also contain werewolves and vampires, depending on how you depict them. Another type could be people being controlled by a parasite.
Sentient: These people are aware and able to control themselves, but they do it anyway. These aren't always creatures that cause wanton destruction, they can even be normal people put into a situation where they harm everyone around them. Vampires, Werewolves, Undead, and plain old Demons can be part of this, and in some cases, the normal people who are forced into this could very easily jump the slippery slope and kill because they want to, or because they support the Big Bad.
The Big Bad: Basically, the guy behind all of the evil in the world, or the main antagonist if they're trying to kill everyone or whatever. These can be land-grubbing evil emperors or evil magicians seeking immortality or godhood.
However, in my opinion, clearly defining a character as pure evil can be cliche and a little narmy, especially if your character is so good that angels think he's good. A good story to me usually has characters that are good and bad, but stray more into the gray areas of morality, that evil emperor could be trying to save his overpopulated people, the hero could be in the situation because he likes to fight. Ultimately, it's all up to you.
(As an addition, you can have gray and gray morality in regards to hero and antagonist, but if you really want pure evil, have them cross into the moral event horizon, which is the moment that a villain becomes irredeemable. This can be killing a city full of good people, blowing up an orphanage that you spent half the game helping of your own volition (making it a side quest), releasing or becoming the very manifestation of evil, or stealing the last poptarts from the hero's cupboard. Just have fun with the story and see where it leads you.)