Wow, there are a lot of these in Anime. And I'm not even counting the "good-guy criminals" or the antiheroes. There are some serious villains whose stories revolve around them, making them the protagonist of said story.
There is Ainz Ooal Gown, the titular MC for the series
Overlord. There is Alucard from the
Hellsing series. And there is Light Yagami from
Death Note. And Revy from
Black Lagoon. Almost too many to choose from.
Also, if he had been more of a lead character, I would have mentioned that Scar from
Fullmetal Alchemist is an outright villain to whom you begin to sympathize with to a large degree by the end.
If I had to choose a current favorite, however, I think I'd have to go with Tanya von Degurechaff, the title character from
Saga of Tanya the Evil, (known in Japan as "
Yōjo Senki", or "
The Military Chronicles of a Little Girl"). Unlike most of the other villain-protags listed, I find I actually
want Tanya to succeed in whatever nefarious plans she has, because I do not think her plans are any worse than her enemies'. She is indeed a monster, on par with the worst of those depicted in similar stories, but I am fascinated that her ambitions might actually have some benefits to her comrades and allies, possibly doing more good than harm, by accident more than design or intent. I anxiously await to see where her story leads.