What's so cool about Vergil eh?
First of all he is Dante's twin (big) brother.
He idolized Sparda and awakened his demonic powers before Dante. In a sense he is the opposite of Dante, while being as cool as him at the same time (it's a different type of coolness).
Unlike Dante, Vergil doesn't view guns as weapons for a true warrior, he relies only on Devil Arms and Summoned Swords (which are projectile swords in a sense, Nero uses them too).
He is the guy who doesn't offer charity to demons. Everything that annoys him dies instantly. There was a boss in DMC3 that Dante had some difficulties with (although he won) and Vergil killed it in a flash.
He wields Yamato and uses Darkslayer, but not the Darkslayer in DMC4. In DMC3 it is the power to transport instantly wherever you want, whether it is up, down, front, back, etc. You could say it is the opposite of Devil Bringer since you transport near the enemy instead of getting them to come to you.
Vergil lusts for power. And knowledge. But what made him the bad guy is that he uses whatever means to achieve that goal. He is Dante's eternal rival, the only one who was a match for Dante except the Devil Emperor that Sparda defeat.
Also here's a video from Vergil's opening in Special Edition of DMC3. Do not worry about spoilers, it actually has nothing to do with the story, it was just added in the Special Edition to make the player feel that he plays Vergil's storyline.
www.youtube.com/watch?v=I5161zG5z78