Has to be Boca v. River. In no other country will you find so many people for two teams. Though statistics say that only 40% of the population is for Boca and 32% is for River, having lived there I'd say it's higher...more like 50% for Boca and 40% for River. Also, they have a lot more tradition than some of these other rivalries (been going on for about a century now), and a history of really quality players (used to be the best league in the world). The fans are absolutely nuts there, watch the waterfall when Boca scores. Sure there's more violence in Turkey or Serbia, but they don't have the history and tradition that the Argentine teams do, Not to mention you can be extremely passionate without being violent. I'd say the Argentine fans are more passionate, less violence is permitted there. When players score in a 'clasico,' often times they don't celebrate and fall to the ground crying instead. It's not like that in other countries.
Independiente v. Racing is pretty huge too, it's Argentina's second biggest derby. But not nearly as big as Boca River.