Speaking as one who has fallen prey to the Lure of Loki....
I wouldn't say it's villain worship in general. It's Loki. Not just that, it's Tom Hiddleston's Loki. It's not just because the fans think he's hot, or because of the costume, or even because they're fans of Tom outside of his roles (though Tom is one of the best actors I've ever seen).
I guess it's the delicately crafted writing that brought the character alive, and the skill and subtlety with which Tom Hiddleston turned Loki real. The character who sounds at first like a run of the mill villain is actually a very subtle and complex person that people empathize with. I guess I agree with Mx Rabbit I like understanding my villains -- and Loki is one whom we understand so thoroughly that we can put ourselves in his shoes.
Loki isn't after power for power's sake. He's after self-actualization.
Loki is simultaneously an Asgardian and a frost giant -- the former by how he was raised, and the latter by birth -- and he's torn, because the man whom he regarded as his father raised him to hate the frost giants, and thus, hate himself.
So Loki's always been a bit of a trickster. He's not inherently evil. Though he does love spreading chaos through his pranks, they're ultimately harmless. Despite the chaos, Loki is also subtle and wise, and understands people far better than Thor, who tends to wave his hammer around and shout a lot. As with the Even though sometimes Loki knows better than his brother, Thor still gets all the attention. Loki has always wanted to be respected in his own right, and not just be Thor's shadow. Therefore, he wants the throne of Asgard -- NOT for power -- but because by stepping into his "father's" shoes, he feels that he'll have proven himself to be a true Asgardian. Thus, he wants his father's approval. While he still thought that he was of Odin's blood, things were pretty normal. Yes, in a society that appreciated waving a hammer around, quaffing mead, and shouting a lot much more than subtle, silent wisdom, Loki felt like the unappreciated tag along brother, but that was it. We can see that he's still devoted to his family -- even though he thought that Thor's little trip to the frost giants was a bad idea, he still helped him the best way he knew how.
When Loki found out that he was adopted, he suffered as much shock as anyone. Not only did he find that the only family he had ever known was
not his family, but that he himself was of the very race that he had been taught from birth to hate. Odin had made it clear from the brothers' birth that the frost giants were their enemy.
Therefore, if Odin hated all frost giants, didn't that mean that he hated Loki as well? So why did Odin rescue the infant frost giant? Was it really pity, or was Loki just a war trophy? So when Loki asks Odin if he was just another stolen relic, what we have isn't an arrogant god demanding the truth from the king of the gods. We have a little boy asking his father whether he still loves him...whether he loved him at all.
...And Odin falls asleep.
The world falls into chaos, and everyone ignores Loki.
Even at the end, when Loki gets thrown off the Rainbow Bridge, it's not because he was defeated. It's because he was so crushed that he let go.
He knows now he'll never get the throne of Asgard, but the reason this matters is not because of the power, but because to Loki, it's a symbol of how his father never took him seriously. So Loki, thinking that his father rejected him, now acts up. The throne becomes an obsession with him, and devoid of his father's approval, he rushes off to crave attention any way he can. This is no different from countless other humans. Loki's basically a very hurt, very angry, and very lonely little boy who's capable of deceiving himself as much as he is capable of deceiving others.
The whole thing begs the question -- if the same thing had happened to you, wouldn't you be as emotionally screwed up inside?
As Tom Hiddleston said, Loki really needs a hug. :-P
And then there's...