The first one I'll mention is sephiroth. Now, he's been overexposed at this point, and a lot of people are rather tired of hearing about him. But many individuals forget just how intriguing he was at the time, as the game kept him shadowed in mystery for the entire first part of the story. We hear his name whispered by Cloud, and by President Shinra, who seem to hold him in reverence. We don't know who this man is yet, but it's clear that he's important. When he does show up, it's one hell of an introduction. Cloud and friends were easily captured by Shinra, and thrown in jail. And yet, when you wake up, the power to the entire building has been wiped out. There's blood everywhere, and if you follow the path of destruction he's left in his wake, you find his sword sitting in the back of the man who, at this point, was the primary antagonist. Where you failed, sephiroth walked in and achieved his goal effortlessly. Bare in mind, we haven't even seen him yet. This is importent, because the game spends a massive amount of time building up his reputation before introducing him to us.
When we do meet him in the flashback, he's a cold but decent human being. We get to know his strengths and weaknesses, and sympathize with him as a person. When he cracks, the game delivers the scene flawlessly. The music is low and sinister, but it builds upon itself as you get closer to the burning of nebelheim. Finally he lays waste to the town, and we're given one of the greatest moments in gaming history.
https://www.youtube.com/watch?v=mrX7aFlSZBQ
The game then continues to build him up. After facing the midgar serpent, an enemy that's unbeatable at this point in the game, we see it killed and displayed as a testament to Sephiroths glory. The game uses the mechanics to emphasize the power of the enemy we're dealing with. It spends a lot of time and care establishing its villain before we ever get the opportunity to actually speak with him. This adds to his aura and characterization, and, love him or hate him, his introduction is nearly flawless.