The kind that is technically not wrong. Where you really just dislike them as a person but they're also kinda right about the situation it just sucks you have to listen to them of all people.
I LOVE villains that are doing what they're doing because they believe they were wronged. For example, Tai Lung1 from Kung Fu Panda and Lord Shen1 from Kung Fu Panda 2. They believe they're doing the right thing for themselves because they were wronged or betrayed by those who were close to them, and those who believed in them.
My favorite parts about these two villains are when they have their "maybe I'm doing wrong" moments. They listen to the other side and almost see the errors of their ways. I think it adds so much depth to their character. Too bad Kung Fu Panda 3 kind of fell flat on this part.
What about Sheriff of Nottingham types who hold supreme executive power and rule with an iron fist, who do battle with the rebellious hero who always bucks their authority and fights the system for the sake of justice?
My favorite antagonists are the ones that are trying to do the right thing but are clearly wrong about it, or the ones that it's clear WHY they're making the choices tey are, and they're not necessarily wrong for them to do so, but they're still following the wrong path. I especially like villains that "could" be redeemable but instead choose to stand by their flawed convictions. It makes for some delicious drama. Another clear favorite is the soldier who is doing something because he feels its his duty, and his loyalty to the Big Bad is stronger than his morals. I like battles between the hero and his mentor where neither is happy about the situation, but both feel they need to partake in it.
I like ones who are foils or some kind of parallel to the protagonist. Sort of like in the Lion King, Simba and Scar have the same want, "to be king", but their idea of how they would go about doing so it dramatically different. This also allows the protagonist (Simba in this case) to reflect on his want. He starts the film with a very superficial view on being king but ends the film with a much more grounded and realistic view on it.
I also like antagonist turn grumpy friend.
I really love traitors~. Any antagonist that used to be friends/family/lovers with the protagonist; there are just so many opportunities for fun banter and awkward situations~. Plus, there's always a chance that their joint character development could come full circle, and they could end up being friends again. ^^
My favorites are reoccurring ones that never quite seem to lose, even when the heroes win. Generally only when the character in question is more in the protagonist's way rather than being truly evil, since otherwise it can be a bit too bleak. When done right it's a great way to have an "oh crap" moment for the audience whenever the antagonist shows up. A good example of this would be the character Sterling from the show Leverage.
I honestly love ally-antagonists! They add a lot of flavor to a story, and they can kind of be the result of a major plot twist. Ally-antagonists can also add secondary conflicts that can illustrate a main point or climax in a plot. Plus, you wouldn't actually expect it, as they would be acting like an ally at first, but then they'll suddenly turn against the protagonist/s, spicing up everything about the story! I love all ally-antagonists though; because there are some that were ALWAYS antagonistic and were already planning something dark from the start, but there are also some that were really allies at first, but then they make a regrettable decision that makes them antagonists. Either way, I guess you can say I'm just a big fan of plot twists! 
love a good villain 
the ones that are not crazy or psychotic but a genius in their own way. sadistic, methodical, perfectionists...
and the ones who have a one track mind. ones that you know what they want just by looking at them... eek!
I really like villains of circumstance or villains where you can really understand why they're doing what they're doing. I like the moral ambiguity of it and seeing how people interpret the different sides of the conflict. It's something I like to write but not actually see as often 
I tend to really like the charming, intellectual powerhouses with a compelling story. Something where you can understand what got them to that point and even sympathize a bit, but ultimately the end can never justify their means. Bonus points if they're tactically minded, have strong ties to the protagonist, and actually win fairly often in the narrative. Redemption can go either way.
Some that come to mind are:
Megatron, Transformers (IDW continuity is the strongest)
Handsome Jack, Borderlands
Gul Dukat, Star Trek: DS9
Dracula, Castlevania (Netflix)
Makishima, Psycho-Pass
I'm sure there are plenty of others, those are just the ones that came to mind.
I love that moral ambiguity. I want both my protagonist and antagonist to have a similar setup, but what ultimately separates them is the ability to self reflect and change for the better. It's so hard to pull of though!
This is a tricky question for me because there's a difference between the villains I enjoy writing and the ones I enjoy reading. I've always been a sucker for charismatic psychopaths. To me, Heath Ledgers Joker will always be one of the all time greats in terms of villain archetypes. Though I do like more classic villains as well. Darth Vader was my childhood, so he'll always hold a special place in my heart.
When it comes to villains I enjoy writing, however. It really depends. For some reason, I really love writing just hideously rotten bastards. Snobby, elitist pricks with zero morales who are constantly cheating, or using underhanded tactics to get their way. Maybe it's just me, but I really love when I get comments on my writing saying how much a reader absolutely HATES the villain I've written and they just want them to die in the most gruesome way possible. That always makes my day. ^^
I really like antagonists who use dark or morally corrupt methods in the veil for the greater good, but is, deep down, doing the things they do really just seeking for something more selfish. Viren from The Dragon Prince is my prime example for this. If done well, it becomes really enjoyable to watch the antagonist's point of view.
My favorite type of villain is one who appears innocent and kind on the outside, but actually is twisted on the inside, sort of like those horror games like Doki Doki and Spooky's Jumpscare Mansion. The plot twist comes, and it leaves the viewer shocked!
I like villains who are complex in their nature; the ones you look at them, see their actions and you end up thinking "man... That could be me, you know? All it'd take would be a single bad day.". I don't really like those stereotypical, completely evil and irredeemable villains unless it is truly necessary to the plot. I think my type of antagonist is the anti-hero one, because they can be shaped and molded by choices and circunstances far more than those characters that were already written into being a villain per se. =)
My favourite kind of characters in general (Including antagonists) are ones who are incredibly one-track-minded, focussing on little else aside from their goal.
My three favourite antagonists of this kind are:
Necalli (A primordial being that exists to consume the souls of powerful warriors - Street Fighter V),
The Lich (A being whose nature leads them to seek out ways to systematically eradicate all life in the universe - Adventure Time)
Augus (A battle crazed demi-god who is obsessed with pleasure - Asura's Wrath).
I find Augus to be the most interesting one because he in no way opposes Asura's quest for revenge and even encourages him to "Walk the path you must". But that same sense of indifference to the causes of others is also what let him stand by while his greatest student had everything he loved taken from him. He essentially has no morals to compromise and operates entirely based on whether he thinks something can entertain him.
"I don't fight for good, and I don't fight for evil. I just fight!" - Augus, Asura's Wrath.
I like antagonists who are actually evil, if they are supposed to be the villain, then I should be able to hate them, cause if you make them into someone who has actual morals or that is a good person (but a little deranged and misguided) then I will end up feeling bad if they don't get a redemption arc...
I like antagonists that are consumed by madness and meet their end because of that madness.
They go deeper and deeper into a rabbit hole. So deep that they can't get out -- they've done some messed up stuff, and while they have their reasons, they're not enough to ever excuse what the antagonist has done. Hell, their redemption might only be met through death.
Even better is the horrible realization that all they did was for naught. It's chilling because you can often pinpoint that moment: maybe it's their facial expression or maybe it's the visuals, but it's clear they messed up, and what they really wanted wasn't something they needed.
And then they break down.
-Chef's kiss- It's beautiful.
Edit: Bonus points if they've managed to drag the protagonist into the rabbit hole. Whether or not they make it out is up to chance, but it's a beautiful hot mess.
Triple bonus points if there's, like, some oddly-enough sensual seduction to the dark side during all of this.
My favorite type of villain is the one that still has a moral compass despite having a bit of an ego. They are warm and empathetic to others, even the protagonists. They think what they're doing benefits the greater good of society, and perhaps it did at one time... but they've become so overshadowed by greed and selfishness that they don't see the impact they're really having.