I love villains with complexity, people who have a reason for what they do -- not just a reason for being a twisted human being, but background motivating the specific expression of wickedness they manifest. If you look at my list of characters for the superhero series Polychrome Heroics, you can see a lot of supervillains and superheroes, along with several who could be either depending who you ask. Their experiences shape them, sometimes influencing the type of powers they develop, and usually touching on their goal(s). So these people do very different things, once put into play.
There's a certain dilemma in backing. Readers almost always want someone to root for. I've read a few very well written books that I don't reread, because the sympathy is too balanced and the story ends badly for somebody, which is unsatisfying. I deal with this in different ways within my own writing. First, I have a range of more and less reprehensible characters. Some of them are downright unlikable; people don't want to rescue these guys, but rather want to throw them under a bus. Okay, we can do that; evil characters tend to bring about their own downfall. But if my audience really starts rooting for one of the more sympathetic bad guys ... things can change. People change. Sometimes there are second chances. In my writing, anyone can be a hero or a villain, and if you change your mind partway through, you can switch sides.
I like to think that option creates more tension and interest in storytelling. Usually the plot positions are fixed in fiction, but in real life, anything goes. People are unpredictable. That element of surprise is exciting.