Although it can depend on exactly how "villainous" they are!

In my current series (which I'll begin posting some of on this website someday!) there is no antagonist. Instead, the majority of complications in the stories involve the protagonists causing problems for themselves, but sometimes they involve a few other characters that the protagonists do not get along with.

However, I don't think those characters count as antagonists or villains. When actually designing those characters, I tend to give them a mix of positive and negative traits like I do with any character, including the protagonists, but they might have a certain negative trait that's particularly prominent.

Also, while they can act irrational, I will sometimes make sure I justify some of the things they do, or give them a bit of a backstory as to why they act the way they do and suggest that they may just be misunderstood and not handling it in the best way. I try to encourage the audience to empathise with them at times too.

I suppose some people might count these characters as antagonists. I personally don't, but if they do count, then they would definitely be of the tragic and sympathetic variety.

When I create a more traditional villain, I tend to go all out and make them completely evil and horrible. I try to discourage the audience from sympathising with them. I do try to make my villains appealing, but in the sense that I try to give them a strong personality rather than in the "likeable if they were a real life person" sense.

I've always had a soft spot for movie/book villains. So I like to give my sympathetic stories. My aim is to make the audience feel bad for them or pity them or at the very least understand why they became who they had become. Sympathetic and tragic villains are my favorite.

In my Fanfics my villains are mostly this, but I do sometimes do a mix of these two options.

Both actually! But I think being able to relate and sympathise with the villains gives them more of an realistic way! And it gives the whole story more emotion if you feel sorry for some of the villains! But pure evil ones are also great for drama :D

I've also written my share of just plain evil.

It gives the villain more character design and I love troubled villains who are struggling between light vs. dark. So good. ^.^

^ Agreed.