Why is it that the Norse god of mischief is so popular? There are plenty of other mischief makers in the world of folklore and mythology, but Loki has somehow made it into the public consciousness when it comes to thinking of someone who will get things properly turned upside down. And this isn't just something that has occurred since Tom Hiddleston played him in Thor or The Avengers . . . this is something that happened before that.
It is possible that he has done so not only because he is someone who is so very good at getting himself and others into trouble, but he is also someone who is good at getting them back out of it as well. When he made sure that the gods of Asgard were no longer able to eat the golden apples that would keep them immortal (of which they had to eat one every day, or else they would wither away and die), he also made sure that they were able to get their golden apples back. When Asgard needed a new wall around it to make sure that it was safe from attack, it was him that made sure that the wall was built ... and then, he was the one that made sure that the Asgardians didn't have to dole out their payment for the wall. The stories go on and on about how he manages to walk the line between doing things that the others would have been angry with him about, and doing things that they would be grateful for.
But it could be that he is so popular because of his connection to the end of the world. The story goes that after Loki has been bound to a rock with a snake dripping venom onto his head, he will one day manage to break free from the bonds that have kept him there, and once he is able to break free, he will start making sure that the whole world is destroyed. Giants, gods, and an army of dead will all meet up for one final battle; this battle will not only destroy all but two people in the entire world, it will kill most of the gods as well. But once it is over, the two humans who survive, as well as those few gods who are meant to rule over the world after it has been burned to nothing will be able to start recreating the world. What makes this story have a happy ending is that the world that comes after the destruction is supposed to be one of peace and harmony; so, even if things have to be horrible in the first place, afterwards, they won't be so bad.
So, it could be that even though it is because of him that everything is destroyed, it is ultimately because of his actions that the world is able to enter into an existence of peace. Could it be that this story is something that could have latched onto the imaginations of people and made him become more popular than he might have otherwise been? It's entirely possible.