TL;DR Vaas is my favourite villain because you form a relationship with him.
One thing I've always been more drawn to than the hero in videogames is the villain. As fun as saving people is, and as awesome as it is immersing yourself in the World you're shaping, the adventures you're embarking on, and the fruits of your labour, the catalyst for your heroic actions (the villain) has always been something that either makes or breaks a game for me.
"Are you enjoying my sister's company? Hmm? She's gonna make a warrior out of you? You are so fucked, Jason"
In a game like Far Cry 4, you are a guy trying to fulfill your dead mother's wish and get caught up in a civil war. The action is cool, choosing to free or enslave your people is awesome, and the interactions between key people and the warriors of Kyrat is captivating. With all that, however, comes the main antagonist: Pagan Min. Pagan Min, to me, was not prevalent enough in the story to make Far Cry 4 game of the year, despite how much fun I had playing it. He radiod you in every now and then, he made only 2 appearances during the entire game, and he didn't feel like he was really a catalyst to your actions.
In Far Cry 3, however, you are captured by Vaas Montenegro. Vaas taunts you, kills your brother, sells your friends, and sets you free to hunt you down. You escape, and you establish him as the catalyst for the events to follow. Throughout the game you run into him many times, and many times you escape his traps. He also talks about you, calls you 'Snow White', and eventually grows a morbid liking + dislike for you. You face off against him, he exchanges words with you, you fight, you kill him, and you and the character finally think "Sanctuary". However, the game doesn't end, but as the player you feel an almost emptiness in Rook Islands after seeing Vaas die. I personally have never experienced anything like in video games before, and because of that my favourite videogame villain is Vaas Montenegro from Far Cry 3.
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I think it might be Anton Herzen from Professor Layton and Pandora's Box. Well, he's technically a villain but as the story unravels you realise he is just a victim, which is quite sad :(
Also, friggin badass Layton swordfight = Professor Layton in Smash 4, which would make me cry with happiness