Pretty simple concept really. A person or group of people is antagonizing The World and the hero appears to stop them. But there's plenty more to it than that.
Sure, any yahoo can proclaim themselves Your Enemy and go on a rampage (I'm looking at you, Team Rocket), but it takes a special kind of sadist to manipulate the powers of creation for their own sick pleasure (hats off to Kefka of FF6, folks). So what's it take to make a villain that's more than just a barrier to the progress of the player? What traits does the Big Bad have to have to make them truly scary, or dangerous? Or both even. What is it that separates the mildly annoying from the truly problematic?
Obviously this idea spreads beyond the scope of just video games, but it's just as important here as it is with any literary device.
One of my favorite villains is Fou-Lu from Breath of Fire IV. And what I feel made him especially effective in this role was that he was impressively human.
Let me describe the character a bit. Fou-Lu is a Dragon in human form, much like the main character Ryu has been in all Breath of Fire games. In fact, you spend several chapters playing AS Fou-Lu as he escapes capture and attempts to recapture his kingdom. At first he cares very little for the lives of those around him. He is centuries old, why should he care about the mortals around him? They are little more than subjects to his court.
Fou-Lu spends most of the game running away from a very powerful sorcerer and ends up wounded. He is rescued in a peasant village by a kind girl. She takes him in to her home and heals his wounds, asking for nothing in return and only offering kindness. The perspective shift for Fou-Lu is simply incredible.
Eventually the girl is captured and Fou-Lu is forced to run again. As punishment for protecting him, they use her as a sacrifice for their ultimate weapon, which they use on Fou-Lu directly. And while he's reeling from the blast, he finds the bell that the girl always wore. It was a strange thing indeed for me to root for the "bad guy", but this scene removed any hatred I might have had for him. And his wrath was mighty indeed.
This character is one of the most unusual villains I've encountered, and I was deeply impressed by him at every turn. He was surprisingly human, which I feel is lacking in most works.