I tend to like obviously evil characters that are hammy, overtly ambitious, badass and cunning. The kind that belittles anyone around them and justifiably so because they are more powerful than mere mortals. The ones to indulge in some terrific evil laughter to show pleasure in their villainy.
Notable examples: Ganondorf (The Legend of Zelda), Hades (Kid Icarus), Gangrel (Fire Emblem), Palpatine/Darth Sidious (Star Wars), Asura (Soul Eater)
I also like villains of the tragic kind or anti-villains. Ones that have not always been evil, but were misguided somehow. Or maybe they do have good intentions, but their methods to achieve their goals are too cruel and destructive to reasonably justify them.
Examples: Light Yagami/Kira (Death Note), Zelgius/The Black Knight (Fire Emblem), Darth Vader (Star Wars)
As long as the villain:
- shows competency, as in, he/she is capable of achieving his/her goals before their eventual defeat (assuming it happens, of course)
- is genuinely shown as a threat, as in, he/she is feared by other characters and is shown to possess a lot of power
- well-characterized as a character, as in, his/her motives and goals are explained
I will like him/her. Those are the bread and butter of a good villain. The omission of the third criterion can also have some interesting results, as it makes the villain more mysterious and sometimes may make the character even more scary.
An example would be Grima from Fire Emblem: Awakening. He's competent and ends up causing major trouble to the world. He's definitely a threat and is feared by the heroes, and he's quite powerful as well. His characterization, however? You don't know his goals aside from destroying humanity, but he's not doing it for pleasure. Whatever his motives behind his desire to destroy humanity are never explained, which ups the creepy factor he has. Overall, eldritch abominations have this sort of dynamic going for them, in which their morality is never clear and may be downright alien to us and the characters.